You need the optional EX primals done (except Thordan) and Main Story 3.1 complete too, this isn't because The Triad is part of the story, It's due to the quest giver probably being Krile, it was said before that she would be play a role in optional content, so while the Warring Triad isn't part of the story, you need to progress in the Main Quest for Krile to appear.