In a team payment that is split equally between players, only the captain can make payment on behalf of the team. We always recommend having multiple team captains in case one can’t make payment a particular week.
In a per player game fee structure, both the player or team captain can process the payment on behalf of each player. If a player/parent has pre-paid for the game, this will be indicated on the captain’s screen so that they do not double-charge that player.