My guess would be that the night shift command officer was left in charge, or perhaps a Bajoran officer other than Kira. There is very little attention paid to the other shifts in most Star Trek series. Sometimes some of the books give them some attention. For instance we learn that Chekov was the night watch officer on Enterprise during the first season of TOS. But those aren't generally given the blessing of canon in the Star Trek universe.
The point is that there are likely numerous officers, both Starfleet and Bajoran on Deep Space Nine that we never hear anything about, any one of which could be left in charge in case the primary crew is absent, asleep or incapacitated.