I've not read of blooming doing anything other than stalling increase in leaf size. Maybe they're growth rate slows down a bit as well while blooming. If the parent tuber rotted it was most likely due to the cold and wet.
They build a new tuber on top of the old (as well as pups) so that might have been too exposed. Hopefully someone who has them actively growing year round will chime in with advice about preventing rot from happening this winter. You could just give them a blanket of mulch.
