Accidental plumbing leak. How bad is this? What should I have my contractor do?
I'd give the contractor a chance to fix things. Your house isn't going to collapse into mold and mush over one event, but you do want to be sure that things are thoroughly dry and that there's no sagging of the drywall or severe warping of lumber. 

I'd expect the contractor to have fans going in several places, especially in the ceiling joist cavities. I'd expect them to express real concern and a desire to rectify the situation.