Q.What Do I Place A Rootless Bromeliad Pup In?
You mention to take the bromeliad pup and tie it to a cork board or branch and let the medium dry before watering it in its tiny cup. I don’t know if you mean to place it in a cup with soil or water? What do you mean by medium? Also by tying it to a branch what do you mean? A branch that’s planted in soil? Or by tying it to a cork board, how do you do that? A vertical cork board?And where does the cork board go? I feel I have more questions then I do answers. I appreciate the help sorry for all the questions.

Certified GKH Gardening Expert
Some people like to mount their bromeliads (corkboard, branch) like you would a staghorn fern or even an orchid. This article tells how.
https://www.gardeningknowhow.com/houseplants/epiphytes/epiphyte-mounting-tips.htm
The medium is whatever you use to wrap the plant in whether on a branch or in a container. The article you mention suggests a moist peat mixture but you could use sphagnum moss if you are mounting it.
If you are putting it in a container you could use a commercial mix for orchids.
The article says to water it in its tiny cup and it is referring to the cup formed by the rosette of leaves, not the container.
https://www.gardeningknowhow.com/houseplants/bromeliad/growing-guzmania-bromeliads.htm
https://www.uky.edu/hort/sites/www.uky.edu.hort/files/documents/bromeliads.pdf
https://www.gardeningknowhow.com/houseplants/bromeliad/growing-bromeliad-pups.htm