Personally, I think that emerging from the Nest/Bug Central would be considered the first action of a unit's turn. Sort of like a tunnelling marker moving to that entrance - the marker moves, and the unit exits/deploys all in the same action. Of course, given that an emerging unit can deploy up to 3" from the edge of a Nest template, and up to 5" from the edge of a Bug Central template (which is already 6" in diameter), that's almost as good as a regular move.
That said, I'm curious to hear an official ruling. If deploying from the entrance is in fact a "freebie", and the unit can then take two actions from that point, it would have some nasty implications for the MI.