As long as you have your shrimp and such already in the tank before the trigger is introduced, your chances of him going after them will be reduced...
The only thing that I've ever witnessed my male do is go around the tank, and pick the hermits up and make a pile of them in the middle of the tank, then watch them all crawl away. This was more of a playful thing than predatory. I mention this because you asked about coral. They won't bother your coral, but make sure they are glued down. Triggers are very curious, and will sometimes pick up objects in the tank (hermits) and play with them. Once they realize they can't pick them up, they ignore them... Mine has never picked up a coral in my mixed reef. Just making a possible correlation...
Some say BT's are reclusive, some say they are very active. Both of mine are EXTREMELY active. They are out and all over the place at the first sight of light (ambient light before the reef lights come on) around 9:00 AM, and don't go back into the rock until after the reef lights go out at 1:00 AM. Every time I walk by the tank, they come right up to the glass, and flutter their fins at me begging for food. They make sure to swim up to my hands first to see if I have any food, then come right up to my face, and follow me around. If I take too long to drop the food in the tank, they will go to the surface, and spit water out of the tank at me... Very interactive...
What size tank do you have for them?