If he's immune to psychology in general than I'd say he doesn't have to make trauma rolls. Trauma rolls as I've used them are based on fear, primarily the fear of death. Without that primal fear he doesn't have to dive for cover when bullets are shooting past his head.
On the other hand, he hasn't mastered that fear, he just doesn't have it. Exploit that. He isn't afriad so he shouldn't get the same warnings as normal PCs, feelings of wrongness and danger. His body and mind don't respond to those things because he has no will.