It definitely doesn't make sense if you stop to think about it, but they're not really trying to make it work - just fill in gaps that shouldn't be there. There is no real version of the story where you met the Exarch before you first met G'raha Tia. The CT storyline happened in post-ARR, regardless of when you did it, and anything else is just the story tying itself in knots so it doesn't have to say the player did something they haven't personally done yet.
This is the slightly odd (but consistent) way that the game handles optional storylines, especially if ongoing characters are involved.
The "canon version" is that those events happened at the point in the story indicated by the quest level and possibly the patch where the quest was introduced. In this case, the Lv50 CT quests take place post-ARR, with Nero fresh from his defeat at the Praetorium and 'out of a job', and I believe the recent destruction of the Isle of Val (as introduced in post-ARR MSQ) was also referenced. Cid is wearing his first outfit that he hasn't worn since early Heavensward.
However, if you skip these optional-but-canon quests, the game will not pretend that you have done them (though you should have). Any future references to their events will have variable dialogue, or be written around in other ways - for example, when Nero re-enters the MSQ storyline in post-Heavensward to propose using Omega, players may have previously interacted with him at the Crystal Tower, or this may be the first time they've seen him since the Praetorium. The story dodges the issue of whether we've met him or not because he doesn't speak to us directly, but introduces himself to the other characters who definitely don't know him. Cid has a variable remark either about not trusting him despite the events at the Crystal Tower (if you did it) or a more generic one about Nero having worked for Gaius (if you didn't do CT - in which case Cid hasn't talked to Nero since the Praetorium either).
Another example I like because it's tangled up in a lot of things is the Binding Coil. MSQ characters are involved, and ignoring it makes the timeline messy.
If you did it at the intended time in post-ARR, it ties in with things going on at that time. You meet Alisaie for the first time since the early events of the game, and Alphinaud is busy setting up the Crystal Braves. At the end of the story, Alisaie departs on a journey (referenced in her Tale from the Dragonsong War) and rejoins you at the end of it in post-Heavensward.
If you skipped it or only partially completed it at the time, when she joins you post-Heavensward in the quest Two Sides of a Coin there are multiple versions of dialogue from both Alphinaud and Alisaie referencing those events - but only as much of it as you have personally completed. If you didn't start the Coil quests at all, she says she hasn't met you since the early game.
And then if you eventually return to play the rest of Coil? It still happens at Lv50, with the characters being their ARR selves regardless of what their 'current self' is up to. If it's still undone after 4.4, Urianger is still standing around at the Waking Sands and participating in the quests despite actually being in a coma at the Rising Stones, because this is an earlier version of him from before that happened. And at the end of it, Alisaie is off on a journey she already got back from.
As I said, it gets messy.
TL;DR: optional events are treated as "not happened yet" until you do them, at which point they had always happened at the designated time in the story where they were written to take place - not at the time when you personally played the quest.
Shadowbringers was written with the assumption that CT happened at its proper time, but is forced to allow for the fact that some players haven't done it - but those variations seem to be added as an afterthought, and aren't supposed to be "equally canon" with the proper sequence of events.