@sweetgingersaid After I make a move the site stays at the game. Can I set it so that it goes back to 'My Games'?
Mine does.
It must be something to do with the filters you have set.
I have the "sort by" option set to oldest moves but I don't think that's the answer.
If you scroll down to game status filter and set it to "my move" it should go back to your games page where it is your turn to move