Steve, my plant of Cardiocrinum cordatum has bloomed here twice so far. It
took a four year break between blooming events.
Unlike your plant, mine has never shown pups around the blooming plant. The
pups appear the next year.
In my experience (which is not based on much experience at all), the
non-flowering rosettes ("pups") die down sooner than the blooming rosettes.
For instance, my plant which bloomed last year at this time has no live
growth above ground. It was there earlier this year and has already died
down for the year.
Your pups are probably fine and I would not worry about them. And next year,
the plant now in flower will probably provide one or two more. So be patient
and keep us posted on how they do.
Jim McKenney
Montgomery County, Maryland, USA, USDA zone 7 where the best advice I can
give Steve is to let sleeping pups lie.