A legal “tag up” means that the runner is at a standing start, touching the base, when a fly ball is first touched for a catch. To go behind the base and get a running start before retouching the base (timing it with the catch) is not legal. If you see this you should call the runner out immediately. The ball remains in play and the rest of the play stands, so don’t call time.
[Under OBR the runner is not out until it is properly appealed.]