Hey CONGRATS!!
"Self Fragging" (although illegal in some states still) is either a sign of good health or just the opposite. Some coral when stressed heavily will so this in what is believed to be a "last ditch effort to ensure survival of the species". Like really bad water conditions some anemone will split in hopes that some portion of the original will more to an area and survive.
I'd say it's just REALLY happy and likes you a LOT!
The easiest way is to place the babies in a dish with some rock rubble and net/wedding veil over top (to keep them from blowing out) and let them attach on their on in a few weeks