I'm expecting time travel to be involved - so if we assume the Crystal Tower raids happen at some point in the "current time bubble" of the MSQ, whether that's in the past or future for the individual player, the Enigmatic Figure is from a point in time beyond that.
It's suggested that the Crystal Tower simply "appeared" on the First, so it's possible it somehow shifted in time and space from Eorzea's future to the First's past.
Also, unless there's something odd going on with clones or exact doubles, the Enigmatic Figure's
character data leaves very little doubt as to his actual identity...