The Federation Master had clearly heard of the 'Mythical Coalition' because of her status and knew what kind of organization they were.
After all, it wasn't like there hadn't been any Quasi-Myths within the three Absolute Factions, but because of the Mythical Coalition's overwhelming power, those Quasi-Myths also ended up leaving the three absolute factions and joined the Mythical Coalition.
Moreover, every leader-level figure of the three absolute factions knows about the Mythical Coalition, even though they were warned to stay away from them and never investigate their whereabouts.
Only the Holy King (Myth of Justice), seemed to be a special case for she was allowed to keep her position within the Cardinal Spirit Temple while also being a member of the Mythical Coalition.
