There is a check flap in drain that is only meant to prevent the water in the high loop from flowing back.
A few tips.
Make sure the Y shaped hose joiner is installed properly one hose on top of the other, not side by side. The hot water can cause the Y Connector to sag and a slow drain will occur.
Also make sure the drain line is installed properly, the drain should be routed floor level not cabinet base level. It should be ran through the hollow spot under the cabinet and then up through the base to the top of the cabinet back down to the outlet. If it is not installed in this fashion numerous water in the bottom tub challenges can occur.
See the attached image.
FP DW Drain.png 212.79KB 2 downloads