I hope you remember Faucon, that Il-2 does not model direct link between joystick movement and control surface movement. A colour square you see in your input setup screen does not represent the movement of your virtual control stick, but a force your "pilot" applies to it (at least that's how it worked up to 4.09, the new patch changed something over here, but I don't know what exactly, becase the readme is a bit messy to understand in this regard
).
Perhaps that shouldn't result in a respose delay anyway, but you have to keep all these little details in mind when doing your tests.
Cheers