I'm no expert on running the Vault event, as I have only done it a few times but on a run I did today we got to the second door and remodulated the energy cores, protected Obisek, and got the door action bar all the way full. The only thing left to do was "Secure the Reactor Core".
We destroyed all the Birds of Prey, there was nothing left except the infinitely spawning fighters. We destroyed the last Bird of Prey with about 20 to 30 seconds left on the clock, and were flying around killing fighters wondering why the timer was still ticking down.
If Obisek fills his action bar, and unlocks the door, why doesn't the timer stop?