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.
Is there a rule that vampires don’t have reflections? I can’t find it, but I don’t have the books.
It’s a common trope in media and fantasy lore, Quite a few tropes of vampires are listed in the flavour text, rather than the statblock, and this is one of them.