Are those soap bubbles on the rubber connector, too? It isn't sealed well. As plumbed, the drain line (trap arm) will fill up with food particles and crud, and block up. It has to flow downhill from the output of the trap.
Actually, there is no good way to connect whichever side gets the dishwasher. I would use two "P" traps on that installation, but the "branch tee" is still going to make that one hard to connect properly.