He said that you need to apply the rudder as you move the stick, as it corrects for the difference in drag of the ailerons... Nothing to do with actually being in a turn, as the other 6 or 7 instructors had mentioned
Yes. And the difference in drag is what causes the adverse yaw.
Adverse yaw will occur if the rudder/aileron inputs are not balanced while rolling into or rolling out of the turn ie while the ailerons are deflected to roll the aircraft. It doesn't happen while the turn is being maintained at constant bank angle. So you are right - its not to do with being in the turn.
(I'm ignoring more subtle effects like the need to hold-off or hold-on bank in the turn in some circs, when you would still need that little bit of balancing rudder).
In normal flying you should never move the ailerons without moving the rudder and vice versa. Its particularly important to get this right when flying in turbulence because if you dont get it right the nose of the aircraft wanders all over the place which increases your passengers' discomfort!
In gliders you'll find that a tiny bit of pro-turn rudder is needed while maintaining the turn to keep the piece of string in the middle, but this isn't the same as adverse yaw, its simply to keep the glider aligned with the changing direction of the airflow as the aircraft turns - powered aircraft need this too strictly speaking but you really only see the need for it in gliders where aerodynamic efficiency is so important.