EUREKA (hopefully) ...
Was thinking hard to figure out how the water seeps in through the door. Moved my hand over the border of inner cover of the door and noticed a considerable gap between the cover and the door at the side where they have hinges (towards speaker end.) Realized that the cover was not properly attached hence leaving that gap.
I think that's the most probable reason how the water seeps in, if you get what I mean.
Wanted to open the entire cover to fit it back, only to realize that the screw inside speaker compartment was not there at all. May be when the winder was changed last year, the service guy didn't put that screw. As I put a screw there and tightened it, the cover moved back perfectly in its place leaving no gap between it and the door. Now hoping that if at all the water moves in along the door border, it won't get inside the door cover, thereby landing inside the car (on the front mat.)
Keeping fingers crossed now.
If the water still seeps in, then may put (paste) a plastic to the lower end of the door (from inside) in such a way that the water just won't land up on the mat. Hopefully, I won't have to go for this workaround.
Note - my guess is that the water shouldn't come down to this point at all if the beading is good. What say guys?