I think we are nearly there, so I hope I don't confuse things further...!
In Aperture Priority mode, the sub-command dial (the front one) allows you to choose the aperture value you want - let's assume you have (as you mentioned) chosen f/11. Turning the main command dial (the rear one) then has no effect - UNLESS you have Custom Setting b5 Easy Exposure Compensation set to "on".
If that is the case, turning the main command dial will apply positive or negative (depending which way you turn it) exposure compensation. Since you are in Aperture Priority and have fixed the f/stop that you want, it does this by adjusting the other half of the exposure equation - the shutter speed - to give you the higher or lower exposure value (EV) that you are looking for.