When opening a waterlogged trapdoor the water can flow out of the bottom. The problem starts when you have multiple waterlogged trapdoors next to each other in which case closing the trapdoors will not result in the water below to disappear. This is the case for all variations of trapdoors.

Further testing has revealed that if there is any kind of flowing water next to the flowing water underneath the trapdoor, the water will not disappear after closing the trapdoor again.

The magma bocks underneath are just to show that the water is not composed of water sources