Unlike with film ISO is a variable in the digital world. That can lead to serious problems.
For all intent and purpose you need to control the ISO before you do anything. ISO if setup incorrectly can limit the camera aperture/speed settings. Personally I like a fixed setting, 400 ISO. It is relatively high but this setting will not create anything like noise nor reduce the camera dynamic range.
At other times I use a range 100~800 ISO because I just do not have the time or do not care.
If you leave ISO on auto there is no telling what setting the camera will use in any automated mode.
Something interesting to me is that you have a hidden '1/3 auto mode' the: ISO mode. How do you use that one? Simple, place the camera on manual and leave ISO on auto. Set your A/S as needed and ISO takes over.
The funny part (to me) is that folks complain that their camera does not react the same way every time they set A or S mode. They just forgot to set ISO on manual... As I said 'hidden'. What they set is really a 2/3 auto mode based on a single setting: the A or S mode the other two are, well on Auto.