So in that scenario the time travel back 3 years alexander is actually standing atop the original version of itself still below the water. Makes more sense since it leaves an Alexander there to be explored.

Aura 'Summoning' with codex-never actually happens, just Goblin summon travelling back.
Goblin Summoning guided by journal
Goblin Summoning travel back 3 years and drops off journal.

The first goblin summoning would need to have been done without the journal. And the first Aura summoning would still need to fail in a vacuum without the time travel.

Aura attempt and fail. Codex broken.
Goblins find codex and fix, use to summon.
Goblins have it rough, time travel, drop journal allowing for a much smoother attempt the next time starting the loop.

Aura attempts, Goblins travel to this point to make sure codex breaks, provide journal to past selves.
Goblins with journal get codex bits and summon Alexander. Repeat as necessary to get desired result.

Pet cat interferes with journal handoff, causing the time loop to break down. It can be guessed that the original journal was way more complete for the Illuminati leader to use, but the cat caused it to be dropped earlier than if the gobin had kept to the point of dieing at the control room.

So each time the illuminati let the invaders get farther so that they can get another chapter of the book filled out, travel back, repeat.