Yeah, I wait about 10 days usually. Very pretty anemone too, btw. Congrats!
As to the question of how often they split, the answer as is so common in this hobby, it depends. Sometimes they will go years without splitting, growing larger and larger. Some folks have them at almost 20 inches across. My first one didn't split for about two years and was maybe the size of a small dinner plate. Since then, he has split several more times. Some believe the splits follow some significant change in the environment, like a major water change after a period of no water changes. Also, when they get really large they seem to just split regardless of an environmental change. If you are interested in more on this topic, on WetWebMedia you can search and find an article where an aquarist gives his recipe to successfully trigger splitting. I can't recall the specifics, but it's something like feeding silversides 3 times per week with no water changes for a couple of months and then doing a large (maybe 50%) water change. Sorry I can't recall the details, but if you search that website you can likely find the article. I suspect there are articles on RC with similar info.