On Possession/Baths boards, each Possession turn Bath triggers for 2VP tokens which should be transferred to the player who played Possession according to recent rulings (below).
http://forum.dominionstrategy.com/index.php?topic=16860.msg674518#msg674518
http://wiki.dominionstrategy.com/index.php/Baths
Online it appears to be the opposite. I played a game where the player getting possessed took the Baths tokens.