How can she lead a group that rebelled and went with Fionna? It seems like Viviene's title is self-styled.
From all that it amounts to in the game, it probably is.
That we see several mages who were either part of the Aequitarian or Loyalist factions who either ended up on their own or were forced to join the Rebellion because they had nowhere else to go, seems to suggest that for all her talk of being the leader of the "last loyal mages", she's far too busy hosting her galas to actually lead efforts to bring those desiring sanctuary under her banner.
Vivienne can best be described as the leader of the Loyalist mages who are still in the Circles with the Templars that didn't go rogue. For anyone who was a Loyalist, an Aequitarian or Formari who had their Circle fall, their fellow Mages or the Templars try to murder them and had to go on the run... well, that's bad luck for them, I guess?
They really should have taken more time to explore her position as the leader of the Loyalist faction or as the counterpoint and foil to Fiona's position as head of the Rebels. She should have been far more of a player in the resolution or aftermath of the war (however it played out) than what we got, especially since her personal questline (ignoring the book collection one, which was more of miniquest) did not involve the Circle, but was rather to help her brew some magic red bull for Bastien.
A throwaway line or cutscene where she was shown to be organising something would have been enough, as well as explain why she too was absent from the Conclave, despite apparently being someone who would have wanted it to succeed and end the war?