I suspect that DBCherry is holding rudder in the turn, which will certainly cause it to tighten up. The proper use of rudder is to simultaneously apply rudder and aileron to bank into the turn. Then once the bank is established, move both controls to neutral. In steeper turns some up elevator is required to keep things in balance. To stop the turn, simultaneously apply rudder and aileron to level the wings.

That being said, a wide flat wing like the cub will tend to over bank if the turn is very steep because the cub, like most full scale light airplanes, is spirally unstable. Usually a little more up elevator is sufficient but in steep turns, a little aileron against the turn may be required. In that case, a little rudder opposite the turn simultaneous with the aileron is correct.