In team play, when does a team score points from controlling a battlefield - on both teammates' turns or only on the controlling player's turn?

Ruling: A team only scores points from a battlefield at the beginning of the turn of the player whose unit controls that battlefield. If your teammate controls a battlefield, your team does not score during your turn.

Nuances:

• If a teammate's unit is moved off a battlefield during your turn, you cannot score by moving onto that battlefield (you can move there, but get no point)
• Neither player on a team can score on a battlefield if their team already controls it at the beginning of their turn