Paul,
Unfortunately it is creating the one pup from the cup, not regrowing, making it difficult to remove without killing off mom. It's best to leave it & hope that it will pup some more on the base. This as far as we know is normal for very few varieties of vrieseas including splendons, splenriet & hierolglyphica and for Guzmania Sanguinea. There may be others that perhaps more knowlegeable members can inform us on. You are correct in that most pups do arise from the base of mom. Hope this helps.