Were this controller really a PID controller then tuning would absolutely be necessary. But this isn't a PID controller - it uses fuzzy logic and my understanding is, appropriately enough, fuzzy. As the controller does have an autotune function I would assume that some sort of tuning is necessary. I would do an autotune. That should reduce your overshoot immediately. Even if the controller has algorithms that allow it to refine the 'tuneset' as it 'learns' you can shorten the learning period appreciably if you give it a good starting point.
The tuning parameters depend on the thermal mass of the load, the rate at which it loses heat, the rate at which the heater can supply heat and the rapidity with which the temperature of the load can change. Thus, and this is a common problem with PID control, a system tuned on 5 gallons of water isn't properly tuned for 6 gallons of mash.