The job quests seem to be totally disconnected from MSQ story flow now, so I'm not even sure they'd bring up the concept of the shards and the Thirteenth at all, let alone fragmented souls, because someone might conceivably be doing it before they've even left ARR.
Though I suppose you can subtly gate it behind story by requiring certain locations for quests, like the dancer quests travelling to Ishgard and Ala Gannha forcing that much MSQ completion before you can access the destinations.