Keeping it as simple as I can
Adverse aileron yaw is caused by the ailerons being up on one side and down on the other giving a difference in drag due to being in different pressure air, this will only happen when the ailerons are deflected i.e. as you roll in (and is usually compensated for in modern aircraft by deflecting the ailerons different amounts up and down - have a look on your next walkround how much more they go up than down at full deflection).
Spiral instability occurs when you are established in a turn so the two things happen at different stages.