when i play multiplayer we tend to say effects like that check every player, as it is a sweeping effect without a target ( think of magic the gathering, wrath of god destroying creatures with shroud. doesn't target, but still gets the effect) we say you have to check it against all the players.
as for action reversing, we say it goes around but if a player declares to reverse then no other player can respond, even if the player only reverses once on a multi.



