Be careful when watering the cups. I assume as u nurture your pups to health that you are keeping it indoors. Standing water will cause the leaves and any blooms that try and develop to rot. Broms actually do not require any more watering than an orchid. They are a low to moderate water plant. Therefore too much water in the cup can actually hurt more than help.
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oops forgot to add. You may need to be patient depending on how old the pup is. A bromeliad pup can take a full 2 yrs. to bloom. It does sound like your only about a fourth of the way there.