Usually, by the time you buy a product labeled as compost it's broken down enough that it's safe and ready to plant. If you don't have anything that needs to be planted now, then you're done.
Think of the material you've just applied as food and shelter for your soil organisms; they'll take care of things below the surface so all you really need to worry about is what's going on above-ground. As long as these organisms have what they need to survive, they'll stick around and be your unseen helpers. Once these materials are gone, however, they'll be forced to leave and find food elsewhere, so replenish your compost once you no longer notice its presence in your beds. Since you're in an especially windy area, moistening your composted beds would probably be an excellent idea. Once again, though, to save yourself a big hassle later on, keep in mind that damp compost exposed to light is where seeds sprout best. Any seed that is already in the top layer of the compost now, or gets dropped into it later will want to sprout -weeds included.
