I always thought Red Mage screamed "Created by Survivors of Mhach and Amdapor!" considering Red Magic is created by using both Black and White Magic which are limited to a select few people in the world who can find and obtain a White Mage Soulstone and a Black Mage Soulstone. if Sharlayan had a lore being that they are created by survivors of Mhach and Amdapor it would be more logical that they created it but so far no lore points to that.
Now it is confirmed that the Red Mage originates from Survivors of Mhach and Amdapor due to a few managing to avoid the Sixth Umbral Calamity that destroyed their civilization. I am curious how much reference will the Red Mage Job Storyline have to the events of Amdapor and Mhach now that we know there are survivors of Mhach and Amdapor. Not to mention possible few small dialogue adjustments for players who completed the Mhach Raid storyline, Amdapor Dungeon, Black Mage 3.0 storyline, and White Mage 3.0 Storyline.
Looking at Red Mage lore there is no "Witch hunt" that happened after the Great Flood but that Mhach and Amdapor survivors swore to cast aside their old Black Mage and White Mage ways to create a new Mage Organization that works together using both Black and White Magic to benefit the world. However, as the Mhach and Amdapor lore states survivors were very few so I can guess the knowledge of Red Magic did not go very far with so little amount of survivors and the Red Mage Order's history with Mhach and Amdapor along with how White Magic became restricted to the Padjal and Black magic is now forbidden arts to the entire World to prevent another Great Flood from happening again.
Still from how things are it is possible the Red Mage Order went into self exile or remained isolated from the world due to what happened with Mhach and Amdapor which would explain why they choose not to make themselves known to the world else they risk revealing there are survivors of Mhach and Amdapor.
There just a lot of things they go with in Red Mage Storyline now we know they are created by survivors of Mhach and Amdapor along with it being possible this is the first time they began teaching someone from the outside Red Magic due to certain reasons.