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.
I’ve read something along the lines of it being because silver is a “noble metal” (or something like that) and vampires are unholy/foul creatures, somehow making them not be reflected by silver mirrors