Right, if you dont destroy the lucifer, it jumps out at the ten minute and 17 second mark, which is only noticeable if you realise that not all the messages are the right amount of time apart (7 minutes is actually 179 seconds after an event that triggers 24 seconds in)... Following the departure of the lucifer (at 10:17) the mission is failed.
At 10:32, Delta 4 self destructs.
At 10:34, Delta 3 self destructs.
At 10:35, Epsilon 4 self destructs.
At 10:36, Beta 4 self destructs.
At 10:37, Alpha 2 self destructs.
At 10:39, Delta 2 self destructs.
At 10:41, Beta 2 self destructs.
At 10:43, Alpha 3 self destructs.
At 10:44, Delta 1 self destructs.
At 10:45, Beta 1 self destructs.
At 10:46, Epsilon 3, Beta 3, and Alpha 4 self destruct.
At 10:47, Alpha 1 self destructs.
(assuming they're all alive that is)