The agent at the gate does not see if the boarding card has been duplicated in the Admirals Club. Since the flight is under airport control, s/he may assume that all pax awaiting upgrades are present in the boarding area, and start to page them right before boarding at T-30 (and maybe soon T-40 like DL).
Technically, the gate agent shouldn't un-board anyone until T-15, but I understand the confusion, particularly while paging someone and the next guy in line is standing at the gate making comments like, "he's not here, I'd like that upgrade so I can board."
I've seen JFK-LAX pax be fully processed through the gate (although largely standing on the jetway) at T-20 because the agent boarded early, and I've had to hustle to board. JFK has such long taxi timings that I think the gate agents there try to close-out their flights as soon as possible.
Best practice when the upgrade has cleared during airport control (within a couple hours before departure): go to the gate at the beginning of boarding.