From what I can tell, this is a bug, but here's how I got around it.

Restart the mission, and this time don't release the prisoners when you get the prison key. Instead, finish the rest of the mission, including getting the sub key. You'll find the captian on the deck, opposite end of the ship from where the jail is. Once you get the sub key and finish the other primary objectives, THEN go back and release the prisoners. Head to the sub pen, protect the prisoners, and jump on the sub.