I'd also like to know why groups are not recognized in Vellum constraints node... seems like a very annoying bug.
Looks like it only recognizes the stretch and bend output groups..
UPDATE:
It only accepts the constraint group groups, and the groups don't transfer by default. There is an easy work around though. Just make sure it's a prim group, and then plug a group transfer node in between the solver and the last vellum node.