After finding all the parts for the generators (two fuel pumps, button, etc.), the proper solution is to press the button, wait for the door to unlock, and then leave through the door.

However, it is actually possible to press the button and then exit the bunker back to the main street before the electricity comes on. After the generators are active, the wires then prevent you from re-entering the bunker and proceeding. Furthermore, this triggers an autosave, but thankfully I saved my game before pressing the button so I was able to reload and continue as usual.

Is it possible to be completely prevented from moving on if one presses the button and escapes the room before the electricity comes on? I wasn't able to find any kind of switch or alternate access to the bunker.