I was trying to figure out how the Atomic 4 was relevant. That makes sense. There are several techniques for recovering a man overboard. Starting the engine would not be my first step. Thowing a lifering would be first, followed by an immediate tack allowing the jib to backwind and circling aound to a recovery position. If I wanted to start the engine at some point (be sure you're in neutral so you don't injure the person or snag a line which is easy to lose overboard in the haste of the situation) I would not wait for the blower to clear fumes.
Situations are different. In light winds it may be advantageous to jibe around. I've been in MO situations where we reacted so quickly all we had to do was head into irons and drift back onto the victim.
In general, though, I think teaching 1 method and sticking to it so everybody is on the same page is the best course, and the first method I described is the one I go with.
Get a good basic book and study it, then practice it in warm, nice weather.
1977 C&C 30 Mk 1 hailing from Port Clinton, Ohio