It is abundantly clear in this episode that the Tuvok's memories that the Voyager characters are exploring are not entirely accurate, at best. The whole attempt by Janeway and Tuvok himself to explore Tuvok's memory goes wrong from the very outset, when the pair do not end up in the memory they were aiming for. Subsequently, things go further "off the rails," to the point where what Tuvok and Janeway are experiencing is manifestly not a memory at all, but rather a new fantasy version of past events, which Tuvok's mind is inventing in response to Tuvok and Janeway's actions during the meld.
So the simplest explanation is that the dating issue is just an error in the way Tuvok is recalling the incidents. He is not in great mental shape as he and his captain go traipsing through his recollections. The critical events (the explosion as witnessed by the Excelsior, then the incidents with Kirk and McCoy) have been compressed together into a more compact narrative by Tuvok's faulty mind.