I don't think it was staged, he looked pretty pissed and I'd be pissed if I was trying to promote a movie, I get there, sit down in the chair and then be told "I'm sorry we're out of time" when he was called there to make that appearance but he is an actor so he could've been acting.
Yeah I assume it was staged. I base that assumption on the assumption that Matt Damon is a good actor. If it was staged then that was a pretty good job he did of getting pissed during the credits there. Pretty funny.