I've read that splitting is a survival method. If it feels endangered, it will split.
I bought a rainbow BTA about 8 months ago. It split twice so far. The first time was about a week after introducing it to the tank.
The second time was last weekend after a water change. Something in the chemistry must have been off between the new water and tank water, because it shriveled up for 2 days, and by the time it opened up again, there was two of them (three total!)
I do feed them once-twice/week. feeding them doesn't seem to cause a split. In my person experience, every time they split, it was a result of them being pissed off.