I've never seen a bubble coral do this, but have heard of it. I have, however, seen many Hammer and Elegance corals do this, and so am not surprised that your bubble is doing so now. And what you described fits the condition to a tee; this type of asexual reproduction usually occurs after trauma to the coral/skeletal structure. Fungia corals are particularly well documented to bud after being damaged.
It takes a while (months) for the detached polyp to form a new skeleton, so shelter it well. Again, this is very cool and I always find coral reproduction interesting.