The rules, in this case are pretty clear. The spell never mentions mirrors or reflections, it “summons illusory duplicates." Spell names aren’t indicative of their mechanical effect. See Chill Touch.
There’s also vampire wizard statblock that has Mirror Image on its spell list.
It would be funny if the spell just failed though.
My ruling would be that the vampire does not appear in the mirror but the illusions do. If someone got creative I would also rule that if you aim your attacks based on looking at a reflection you would be attacking a single target with full concealment (normal attack roll with disadvantage) and not rolling to see if you hit an illusion because you're aiming specifically at where they aren't.