Yeah, it happens. Sometimes they break, and sometimes they don't. I have shot threw small trees, and no harm done. Others, I have hit trees and they explode as yours did. Carbon is stronger, but not made of kryptonite. They can, and do, break.

Shoot another one in the same tree and see what happens if your worried about it.

Nah, I wouldn't worry about it. The tree will most likely survive until next tree hunting season. I don't know how you're going to gut it and get it back to the house though.