We grow a variety of Tillandsia's but we are not experts. We had one two flower and one pup, with the pup and flower now about 6 months old. At first none of them grew well but we increased their light and watering and they grow much better now, when we changed how we treat them the 2 of the same variety, don't ask me to name it, (crescent cross section on the leaves, and the leaves follow contorted growth form).
I feel the instructions on watering is too low. We now water them on the same cycle as our water changes for the aquariums, once a week. They get a bucket of the water from the fish tank, and we place them in this bucket for at least 2 hours. When the plants come out they are softer and larger (leaves not as contorted), they then get placed on a window sill facing North East, but the also get light through nearby South East facing windows. We have about 7 varieties all noticeably growing well now. We no longer bother with spraying them with water. Temp between 65 F to 85.
I've read that the parent plants often pup during/after blooming, but then die. Of the two that bloomed one died soon afterwards without a pup, and the one that lived pupped, but is still vigorously growing. Still in the high learning stage with these plants, so take anything I say with a grain of salt.
My point is make sure they get enough water, I use fish water because I believe it provides some micro-nutrients.