Polo Rules

So the team in possession can cross at any time after all 3 of the scoring are back in their own half?

That's how it was enforced in Florida: refs were meant to brief their teams first games by saying that they would take all players returning to their half to mean that they were ready to play with no verbal acknowledgement needed (teams could delay sending one man back across the line to avoid cheap shots, which many teams did to ensure their keeper was in the net, etc).