The story seems to involve Promathia/Shinryu escaping Abyssea and creating a split timeline in the Sky Realm where the sky is red (and not blue). The captain (that is, the PC) is pulled into a cavernous maw and winds up in this alternate timeline, where the world seems to be intersecting with Vana'diel and Abyssea. I don't know enough about XI to pinpoint where it falls in the Rhapsodies timeline, but everyone (Prishe, Prishe, Ulmia, Lilisette) seems to recognize Iroha (except Iroha).
It's also worth mentioning that Shantotto (because of course she's in it) indirectly references her trip to Eorzea.