According to Memory Alpha, Tuvok was born in 2264, six years after Star Trek tales place, so he's not even born yet. One would imagine that the destruction of the home world of his species would alter history enough that he would never have been born, but I guess one never knows if the universe will still "fate" him to be born (see Chekov)...
Well, if we can buy that the same people would still be born in the Mirror Universe, which diverged from the Prime Universe ages ago (and don't get me started on all those myriad
alternate universes in Trek Lit
), then why not?