Ive had rummynose with neons. Rummys are one of the best schooling fish out there IMO. They are nearly always together in a tight school. If one heads across the tank, the others invariably follow. They rarely stay still for long.
Neons on the other hand (after they get used to a tank) seem to break off into smaller groups and sit in place for long periods. After they get comfortable in a tank their schooling instinct seems to decrease steadily. Not so with Rummys! What I have found is that the neons sometimes will get involved in the schooling behaviour of the rummys, probably instinct kicking in. They see the rummys swimming quickly in a tight school and instinct causes them to join them. Not all of them, but small numbers will often join the rummys for a bit and then break off on their own. (The rummys probably tire them out - Don't bet against a rummy in an endurance race

) I would expect to see similar interaction with cardinals or black neons.