Without a doubt they also reproduce sexually. I don't know anything about how they do that, except how other anenomes do it, but I know they must to maintain the strength of their genes. No doubt there must be certain environmental conditions before they will reproduce sexually. In the end, it doesn't matter much for the hobbiest because they are so darn effective at reproducing asexually. They are also among the hardest to kill because a new anenome can grow from even a few cells, which is why they can't be cut off or squished, you just make more aiptasia.
Perhaps someone knows the specifics of how they reproduce sexually, if that's what you are wanting to know.