Vrieseas do pup from the base of the mother plant after flowering. The mother plant will continue to decline as the pups grow, and the pups can be separated by using a good serrated knife to separate them once the pups are 1/2 the size of the mother plant.
However, buying plants from commercial seller does not ensure that you know what the size of the mother plant was really supposed to be. Many times the mother plant was forced into bloom before full growth. I have a Vriesea 'Tiffany' that was 6" tall when I bought it from Frank's Nursery one year ago. The bloom was out of color, so I got it for $1. The pups ended up being more than 12" tall and still haven't bloomed (actually, I gave one of the pups away, because it was just getting too big in that 50 gallon).
Oh, and they don't reflower.
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Homer W. Faucett III, esq.
Purveyor of Trivialities and Fine Nonsense