I’ve used both tape and RTV silicone sealer. The latter works well and in the event one ever had to go in there again it peels loose without destroying the plastic and is easily removed from the door.
The water leak into the car does not likely have anything to do with that plastic liner though. I would suspect a faulty door or window seal.
Stick a dollar bill about halfway in at various points around the door opening and then clsoe the door fully. Try to pull the dollar out. If it comes out easily then that could be where the leak is at and it may be time for a door or glass adjustment.