He was also a random guest star bad guy of the week on The Next Generation, in the episode "Starship Mine." I had forgotten this, and it is especially jarring when you stumble across that episode after you're used to him being Tuvok.
When Sulu was captain of Excelsior, that's right. I feel like they alluded to this in a Voyager episode, like this was his real first assignment, and then he spent time making a family. So rather than him being a random character in the movie, he was now canonically Tuvok on his first stint with the Federation.
No, in the Voyager episode he is on the Excelsior with Sulu as captain. In Generations he is a bridge officer on the Enterprise B and Captain Harriman was in charge (nominally since his bridge was full of flag officers).