Lots of people have ideas about this, but no one really knows exactly how these patterns form (there are probably lots of ways, really). I just finished a dissertation on this kind of pattern formation in small molecule crystals, and I think it's safe to say that there is no definitive mechanism that applies to every system. (Look up banded spherulites if you want to read more...it's a common morphology in polymers and small molecules, and has been studied for well over 200 years.) In this case, it is very likely that the crystals grow via "rhythmic deposition," very much like you suggest. I would guess that there's a thin film of water on the windshield, and that a small polycrystal nucleates and grows until it uses up all of the water close by, and then has to wait for more water to diffuse into the gap it has created. Since some crystals will have reached further out from the center of the polycrystal than others, they will begin to grow first, creating a new ring with an empty space left between the new ring and the old.

As far as your dark spot is concerned, the seed for the polycrystal can be very, very small, but once growth begins in the liquid film, it progresses very rapidly outward. The central seed doesn't have time to grow very big before it is surrounded by new crystals that use up all of the available water. Also, if the film is very thin, the seed can pierce the surface of the liquid. Once broken, the liquid will pull away from that central spot due to the surface tension of the water, thus leaving an empty hole.

In any case, your mechanism sounds just about right. Even though the center looks dark, I would bet that if you could look very, very closely you would probably find a tiny seed that started it all.