Anyways, I completely unplugged the joystick, fired up the game in expert mode and the helo still rolls to the right way too much that it would end in a crash.
Once I switch back to trainee mode everything is fine.
So it's something within the game. I can't enable/disable certain settings in expert mode so can't track down the actual cause.
I tried to
trim but no matter how many times I turned it on/off the behavior remained.

I got no idea what else I can try, seems I am stuck in trainee mode.

But I want the real thing!
So either that's a bug or I haven't understood how trimming works (if that is the issue anyway).