It was mentioned early on (I won't go looking for the quote tonight) that it's only a hundred years since Mide's ancestor created the codex, so not long enough to lose track of relations. I'm not sure that sounds right from an overall timeline perspective, but it's what we've got to work with.
Stray thought: what if present-day Mide and Dayan are clones of the "ancestors"? There's weird leftover Allagan tech on the Steppe and the ancestors know that a younger version of themselves need to be born to repeat the time loop. If that works and doesn't technically involve the same matter going around the loop again...?
Yeah, this is mostly how I understand it to play out - other than that you seem to be getting your goblins mixed. Roundrox is from the Idyllshire clan and wouldn't have had anything to do with the Illuminati summoning Alexander.
The question of "where it started" is too hard to pin down because it's bootstraps all over the place, but there is no need for Alexander to have existed prior to the earliest parts of the time loop.
As I understand it, chronologically:
1. Alexander appears in the past and drops off Mide and Dayan to found the Hotgo tribe.
2. They live and die and their descendents carry on their work.
3. Three years ago, present-day Mide and Dayan try to summon Alexander out of the aether and instead get time-travelling Alexander from the future.
4. Shortly after the events of Heavensward, the Illuminati summon Alexander - this is the start of its existence in "real time".
5. Alexander runs its simulations, concludes the best course of history is for it to be sealed away, and calculates the events that need to happen to bring this about. Bootstrapping ensues as the earlier parts of that plan "already exist" and have played out chronologically even though from Alexander's perspective, it has not carried out the plan yet.
6. Real time events of the Alexander quest line play out.
7. Alexander is sealed away with Mide and Dayan on board.
8. Current point in time
9. ???
10. Alexander travels to the past to drop off Mide and Dayan (then returns to whatever state it is in as of step 9).