I posit that umbrellas work as such do to a decided LACK of tautness within the entire system, as employed. Sure, the fabric may be stretched across the skeleton frame at varying degrees of tension, but that frame is fairly light and flexible. This "give" allows the force of each individual raindrop to be "taken up" by more parts in the system, besides the fabric itself. Providing even more dispersion of said force is the fact that you're holding the umbrella in your awesome, shock-absorby arm.
Compare this to a sheet of silnylon stretched nearly drum-taut across a set of relatively inflexible aluminum or carbon poles and guyed out with static lines, and I can see why one might experience "misting" with a tarp, while I've never even once noticed any misting under an umbrella...
Edit: Grammatical reasons only.