From what I remember of my type rating,we are not taught to touch the trim release except if you can not get the aircraft settled using the coolie hat. The AFCS though will take care of everything below 40kts and only above 40kts you need to use the coolie hat. I hope that makes sense.
Mostly I fly the machine on the coolie hat or have the coolie hat follow the cyclic.
The Dauphin I used to fly we handled the cyclic and then used the trim release to set the cyclic in it's new position.