
It actually is better to wait to separate until the pups are at least 1/3 the size the mother plant. Small pups don't divide well, but larger pups almost always survive.
You should make the divisions while the plants are actively growing, generally a warm part of the year.
After separating the pups leave them to sit on the counter for 24 hours before repotting. You can dust the roots with a fungicide.
Use a potting mix suitable for Bromeliads or an Orchid medium.
https://www.gardeningknowhow.com/houseplants/bromeliad/growing-bromeliad-plants.htm