I have had a similar experience with new growth starting up stalks, but my experience was with daylilies.  What I did was to keep looking for little roots to start showing on the small plants on the stalk.  When the roots appeared, I cut the stalk and then left a little section of the stalk on either side of the plants.  Then I planted them, and they grew.  The mother plant was yellow; the babies were sports, apparently, as they bloomed red.