It seems to me that it was Americans, start to finish, fighting for themselves that led to the Captain escaping and the pirates being killed, eventually, by the military. Captain Phillips first volunteered himself to the pirates to save his crew. Then, twice, he attempted to escape by jumping overboard. The second time was successful, probably because the Navy realized he might try it a second time and were prepared.
The fourth pirate was on the Bainbridge negotiating the ransom demands when Captain Phillips managed to escape.
It looks to me like the captain did what he had to do to stay alive.
As to what 0bama ordered and when, we know not. Those pirates in that life boat weren’t going anywhere. We have to win the little victories because in this war on terror most victories are little ones.
However, to not follow up by hitting the pirates ashore would be a defeat.