I have played through both Past Imperfect and Doomsday Device. Didn't the player character kill B'Vat in the past. I distinctly remember his younger self telling the player to give him an horable death in battle. After that, him showing up in Doomsday Device seems out of place.
I suppose it could be exlpained that the B'Vat in Doomsday is infact an Undine. The whole idea of endless warefare and strife fits in to their plans very nicely. The counterpoint would be that the player would immediatly identify him as an imposter. Also, the interaction of B'Vat with the player and his actions during the war could easily cause Klingon Intelligence to at least keep tabs on him.
Personally I go with the explanation that B'vat is a timetraveler and the one in Doomsday is a younger version of himself.
So you can encounter him after you killed him in the mission before that from your point of view.
The B'vat in Doomsday however is perfectly free to go on and kidnap Miral Paris after his Doomsday plan has gone to hell.
Is your head hurting yet?
Anyway, that explanation even leaves the possibility open for him to return whenever the devs feel like it.
We could even kill him repeatedly and he keeps messing up the timeline by showing up as an even younger incarnation.