I am using a TOHO TTM J4 S (SSR) controller to drive a SSR controlling a small oven. Whether I select PID or On/Off control the controller always continues to fire to about 10 degrees past setpoint.
Overshoot is an expectation of On-Off control; it's normal.
The On-Off control setpoint is typically in the 'middle' of an adjustable 'hysteresis' band plus whatever over/undershoot the process dynamics support, as shown on this graph for a widely used single loop controller:
If the process overshoots in PID mode, then tuning is too aggressive.
The spec sheet says, "Self-Tuning", "PID Over-shoot protection" and "Auto-Tuning (AT) Coefficient". An AT coefficient sounds like manually adjusted self-tuning. I guess the self in self-tuning refers to the operator's self.
The manual didn't download, so you'll have to check into how to dink around with any or all.