No, the timers are not built in to the powerheads. I have had problems with my power adapters, but that's another story...
I have Tunze powerheads, and Tunze "controllers". The controller is just another piece that connects between the powerhead cord, and the plug in cord. I think the model I have is 6101, but I'd have to look.
Take a look at post # 97 on my build thread and you will see a pic of it...
https://forums.saltwaterfish.com/t/316459/t316s-280-reef-continuation