In most cases there is not - nor does there really need to be - any in-universe explanation for an actor playing multiple characters in the same universe, unless the characters themselves are specifically poised to have some connection. You should especially learn to disregard such coincidences if you really love the Star Trek universe. It is very common for actors to have multiple minor roles in the same series, or across several series, in the Star Trek franchise. It's also quite normal to see an actor who previously played a minor or one-off character in one series taken on for a major role in a later (or, in some cases, the same) series.
As commenters have noted, Tim Russ also appears as a human mercenary in TNG. (Thanks to Xantec for the reference.) Aside from that, and your mention of his role as an Enterprise-B Lieutenant in Generations, he's also portrayed a Klingon mercenary on DS9. Then, if you really want to abstract every Star Trek role he's had, you could also count thirteen variations or imitations of Tuvok himself in VOY.
Another commenter brings up Jeffrey Combs. He's not only played one, but two major and otherwise unrelated characters in DS9 - even once portraying both roles in the same episode. (Thanks to Izkata for that one.) He's also played an Andorian on ENT (Thanks to Mark Rogers.) and several other minor characters across the franchise.
Then there's Star Trek's own First Lady, Majel Barrett, who, aside from being the ubiquitous voice of the Starfleet Computer across most of the franchise, has also portrayed recurring characters in three of the television series - in fact, even two unrelated characters of the same species and affiliation in one. And this doesn't even begin to cover her work in The Animated Series. (Thanks to jwodder, here.)
There's also other multi-character players, like:
(Thanks again to jwodder - who seems to have an odd fixation on the feminine variety in this subject.)
For an example of someone else who got their start as a minor character, and went on to play a (not too dissimilar) major character in a later series, check out Robert Duncan McNeill who played Cadet Nicholas Locarno in TNG before becoming Lieutenant Tom Paris in VOY.
Another one I've particularly noticed has been Ethan Phillips who played a Ferengi on TNG prior to his service as Neelix on VOY, a maitre d' in First Contact (which was released while he was already a part of the VOY cast), and another Ferengi on ENT.
I hope by now it's safe to say I've made my point. Now, cases where one might legitimately expect to see connections between characters portrayed by the same actor would be:
Or, here's a better example of one which would really warrant a question (which I'm sure has been asked about here, but I'm too lazy to look up at the moment):