They shouldn't float up after the first few days. A lot of stem plants take root within days, and some develop surprisingly extensive root systems if not pruned often. The best way to prune stem plants, BTW, is to uproot, cut off the bottom, and just replant the top, since this is the pretty part. Old sections near the bottom will yellow, weaken and lose leaves with time, and you don't want to be cutting off the new growth (the top) all the time. Maybe alternate top pruning with uprooting if you find it too much of a chore.
But anyway, Cabomba will root for you. It also depends on the substrate type and size. Most plants have trouble rooting in large, smooth gravel. Something like Flourite it much better at keeping them down and promoting growth.
I hope you have plenty of light, because this plant needs it.
Good luck