Smash Up Base Game Rulebook, page 7 wrote:
Game Over, Man
At the end of any turn that someone reaches 15 VP, the player with the most victory points wins. If there is a tie for the most, keep playing
turns until there isn’t. No sharing! Except for your two factions. You guys are BFFs.
To clarify, the game will end in that turn; it does mean that if base gets to score as a result, that happens first before the "end of turn."