I am speaking of Nikon cameras here, but Canon and others have similar rules.
The DSLR camera will have metering modes A, S, P, M, and some models also have Auto mode. Differences are:
So realize that Auto mode is "auto everything automation". However, in A, S, P, M modes, quite a few very important things become the choice and responsibility under control of the user. This is not hard, how to use camera settings is just fun stuff every photographer had to learn, and then your control allows the results that you wanted.
Camera automation first meters the ambient, and the camera settings are for that ambient. Flashes have to work into those ambient settings. But we do have other choices, and also, flash can cause a few possible modifications of that, discussed more below.
In camera A, S, P, M modes, you have to turn Auto ISO On to use it. Then the Auto ISO menu has three settings.
In any camera mode, Auto ISO works only as last resort, only when the hardware setting limits are reached, and they have no more range to go, and increasing ISO is the last resort to maintain proper exposure. Auto ISO is Not some optimum combination of settings, but is simply last resort when the settings limit out. High ISO today is not as much problem as it previously was, but if Auto ISO kicks in, the camera settings are at some limit.
In camera S mode, we set shutter speed, and as the light falls, the aperture opens wider. When the lens hits the wide open limit and can go no more, then Auto ISO starts increasing. That means if S mode Auto ISO kicks in, the lens aperture will always be wide open, possibly not the best choice for every picture. And since flash exposure is independent of shutter speed anyway, S mode is not my favorite.
Camera P mode, Auto ISO works the same as in A mode detailed next. So A and P should be combined here, but there are differences. If possible, P mode changes both aperture and shutter speed instead of ISO. ISO is not changed until at two limits. For Auto ISO to kick in, the shutter speed will be at Minimum Shutter Speed, and the aperture will be at maximum, but maximum aperture has another meaning in P mode with flash. If P mode with flash, the lens maximum aperture (widest aperture, smallest f/stop number) is limited by higher ISO and flash. The lens is stopped down 1/2 stop for every stop of higher ISO, the aperture will not open all the way. If Auto ISO has increased, it is at both limits, even if at maybe f/5.6 or f/8. What you see is the current maximum possible aperture. P mode flexible shift mode shifts to other Equivalent Exposures, but it will not shift these limits. P mode seems not the best choice for Auto ISO with indoor flash. However P mode can be great for fill flash in bright sun.
In camera A mode (and P mode), the Minimum Shutter Speed is an added artificial limit, specifically it is the threshold shutter speed when Auto ISO kicks in and ISO starts increasing. Auto ISO action occurs in three phases in camera A mode.
Auto ISO only changes when we hit the hardware settings limits. But waiting until the actual real lowest 30 second limit is reached would be unacceptable, so the Auto ISO menu adds an intermediate Minimum Shutter Speed setting, to be the threshold for increasing ISO. We can set our choice of any shutter speed to be minimum, meaning this is the shutter speed limit that active Auto ISO will always be using (if between Minimum and Maximum ISO). So note that this Minimum Shutter Speed seems a better replacement for S mode with Auto ISO, since it is our choice of the shutter speed that active ISO will generally always use (but the range is greater), and we are also still at our chosen aperture, which S or P mode cannot provide.
Again, this Minimum Shutter Speed is important in camera A and P modes, because this menu value will become The One Fixed Shutter Speed whenever Auto ISO is active. Meaning, Auto ISO values between Minimum and Maximum ISO will always use this Minimum shutter speed (so give it some thought — this is the shutter speed you will be using). Camera A mode seems a milder last resort situation, Auto ISO is often limited at the Minimum Shutter Speed you have selected, and aperture is your selection, but ISO still floats. If still at Minimum ISO, shutter speed may be faster, and if at Maximum ISO, shutter speed may be slower (to force a correct exposure). But if in between, it will use Auto ISO Minimum Shutter Speed. If this Minimum Shutter Speed is too high, you are probably usually at high ISO. If too low, then the shutter speed may always be too slow. The more recent Nikon models add an "Auto" choice for Minimum Shutter Speed, which will use the handholding rule of thumb of the shutter speed being "1/focal length seconds" for the focal length in use. For cropped DX models, this will be 1/(focal length x 1.5) seconds. This seems a good choice, Minimum Shutter Speed will increase with focal length.
Situations vary, but I like around 1/80 or 1/100 second for Minimum Shutter Speed. Actually, I'm old school, thinking ISO is a pretty important parameter worthy of more consideration, so I like to choose and use manual ISO, paying close attention to what's happening, especially true with flash. But for walkaround vacation snapshots, normally without flash, sometimes in bright sun, next minute in dark places, Auto ISO is really handy to make it fast and easy work.
If in dim places, if you want a faster shutter speed than the 1/60 second default in A or P modes with flash, the alternatives are to use camera M or S mode to set what you want, or to go out into brighter ambient that will meter higher (because this case may have actually been metering that 1/4 second).
In camera M mode, we set both shutter speed and aperture, which cannot vary from what we set. Which then may not be precisely correct for the metered light, so then Auto ISO tries to adjust to make the ambient exposure be right, still at that selected shutter and aperture (and Auto ISO affects the TTL flash exposure too). Auto ISO can go below the Minimum ISO in M mode, if necessary and if Minimum was higher than available. So in this way, Manual camera mode can become Automatic point & shoot, so to speak. Some users doing sports photography claim advantage of this, being able to specify the exact shutter speed and aperture they think they need, but allowing any ISO to become an automatic exposure anyway. Of course, they must try to stay in the proper settings ballpark, but I suspect this is subjective. The feature is outright cute, and it does make Manual mode be another auto mode, still giving priority to the settings. But Auto ISO will have less possible range than if also allowing camera settings to vary as needed. We do always need to watch what the camera automation is doing, because if M mode is at Minimum or Maximum ISO (limited by ISO), you may not have a correct exposure.
I would suggest that if with Auto ISO, setting aperture and Auto ISO Minimum Shutter Speed in camera A mode is essentially the same thing as setting same values in Manual mode using Auto ISO. It has greater possible range, allowing a faster shutter in the brighter light (seems no problem), and able to force a slower shutter when maximum ISO simply is not enough (seems better than not). Not all camera models show current Auto ISO in the viewfinder (to notice it), but they show shutter speed (for A mode). Auto ISO seems much more fail-safe in A mode than in M mode. The only alternative in M mode (other than greater user attention) is possibly incorrect exposure.
But camera M mode certainly can be the good stuff, especially for indoor flash where we're usually not concerned with metering the insignificant ambient level suffering underexposure (needing flash).
It seems safe to say that critical work in planned studio flash sessions are always manual camera mode, with low fixed ISO, and with shutter at Maximum Sync Speed, to totally exclude any effect of ambient light. We plan and control the flash lighting instead. Exceptions do exist, using window light for example, which have their own problems. We cannot correct White Balance for mixed lighting, one will be wrong. If we attempt a compromise WB, both will be wrong.
Do consider this: With low ISO, and with indoor flash, maybe you always set A mode and f/5, and your shutter always says 1/60 second. That works, but there is no difference if instead setting M mode and f/5 and 1/60 (OK, one difference, Exposure Compensation has no effect on M mode, it stays fixed). It is still the same exposure for ambient, which is insignificant and underexposed anyway, out of the picture (indoors with flash). And TTL flash is still automatic, even in camera M mode. But except then, you have more choices, to try 1/200 second, or 1/15 second, to control the ambient light more without affecting flash. So play with this, try some comparisons, expand your flash possibilities. In brighter light outdoors, the need to properly expose ambient can complicate M mode, but this is normally no issue indoors where we use flash (speaking of low ISO).
Some users do like a slightly slower shutter speed to add a small bit of incandescent orange in their indoor bounce pictures. It gives them a pleasant warm tone, which can be a planned goal. My own notion is that when you get both the White Balance and exposure just right, there's nothing like the true picture that pops out then. Raw image processing goes far towards easily getting that correct goal.
Two possible issues with camera A mode with flash.