Two ideas. the FIRST is CLEAN the intake filters I have had that issue several times when I'm lazy about cleaning the intake filters and ONE time it was not so my first suggestion is CLEAN THE INTAKE filters. and I can tell you when the blower shuts off it is kind of "Niagra Falls" under the A/C. if that's the problem.. If you need to know why. ask.
Now the other problem.. For this you need to go up on the roof. Pull the shroud and do two things.> Clean everything (might as well since you are up there anyway This includes the condenser coils (On a Dometic I suspect the side that gets dirty is the fan side.. not easy to clean) inspect to see where the "Drip Lip" is (may be on one side or the other or the "Rear" (condenser) side of the A/C.
The one time it was not Dirty Filters the RV was not quite level. the drip lip on that unit was on the rear and I was nose down a couple inches. Lifting front fixed. but .. like that was one of several so I do not think that's it.
Icing of the fins can cause a slow drip drip that will go on for some time after you shut it off.. But not as likely to "Niagra Falls" type downpour.