the way i get it is that in the true timeline (Lilith's timeline), the Shadow Lord's army overwhelmed the allied forces, conflict and chaos never ended and only the fittest who survived ultimately pledged themselves to darkness (Odin), with Lilith being the leader of them all.
Altana, as one of the two original deities to the world, grieved over the major loss of lives in the Crystal War and this caused her to (knowingly or unknowingly) create an entirely different timeline where the Crystal War did end and it'd follow thru into the original storyline for FFXI. This fabricated timeline is no less real than the true one, but it isn't naturally occuring.
Somewhere along the line, tears of Altana that came to possess some living corporeal form (the Cait Siths) decided that they'd take this one step further by summoning Atomos to devour the true timeline so that Altana's alternate one would become the true one - at this point i'm assuming these timeline deviations / tampering with time is common enough that Atomos could have been invented with that purpose. However because he cannot really act independently, the Caits try to nudge Altana's timeline in its favor so it wouldn't get devoured, but it catcehs the attention of Lilith and so she sends her army along to make sure her dark timeline remains intact.