it sounds like there's water going down the window, past the outside rubber and into the door.
Try, with the door trim off and the window down, glueing some weather stripping underneath the rubber, but make sure that you get a seal with the window up. The water should then go to the outside of the door.
Or, seal your speakers in a bit of a plastic box, cut the bottom off an ice cream bucket if you're worried, and attach it to the inside of the door trim
Option 1
/ O existing rubber
| OO new sealing
| door continues on
Option 2
+-------| ice cream bucket glued to inside of door skin
| /
wire through grommet +-- -o< speaker
| \
+--------|