Polo Rules

I was under the impression that the game restarted when 2 players from the scoring team had gone over the halfway line.

This is incorrect. The game restarts when:

the scored on team has the ball under control
all 3 members of the scoring team are in their own half (although they must retreat without delay or interfering with the ball or members of opposing team)
the ball or a member of the possessing team has crossed halfway