When a player sends a move, all players get this notification. And since you are also using sendMoveUpdate on server, players again receives a notification. Therefore your players get notifications two times. You can disable the notifications for first move so that players receive notifications only when you call sendMoveUpdate().
You can disable the sending of notifications by setting the sendNotification parameter of HandlingResult to false in handleMoveRequest of BaseTurnRoomAdaptor.
If all you want is to change the next turn, you can simply use setNextTurn without disabling notifications or using sendMoveUpdate. All players will receive move notification with new next turn.