'Payments will be made to those who had already moved to Universal Credit pre-gateway or who will move over due to a change in circumstances after its removal in 2021.'
That seems to mean the advisor had the incorrect information but thank you for looking into this.
There are several scenarios where you would not qualify but as none of these was mention our Welfare Rights contact thinks the most likely reason is that the DWP person has got it wrong so I would try calling again and hopefully you will receive someone more knowledgable.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems