It's triggered by AI core usage and you need to defeat their crisis three times.
I had AI cores for +18 HA points per month and let HA tick up for about four years for the bar to fill up and reset. No crisis came. I can only conclude that I broke it, that is perma-avert it passively and unknowingly, by either stealing the Synchrotron from Nachiketa and/or the Fullerene Spool from Eventide long before I started using AI cores to try to fight HegemonyMan for its power. I was afraid I would perma-avert Diktat's crisis by stealing the Synchrotron from Sindria, so I went to Nachiketa to steal Hegemony's Synchrotron instead. Did not know stealing any item from Hegemony would break them too.
I do need a forge and synchrotron for my military bases and fuel plant, and the easiest or most reliable way to get those items is steal them from the core worlds. I do build up a raider fleet for stealing blueprints from everyone (and I need massive ground power to stealth raid Kazeron for capital/DEM blueprints), so why not steal their other items that I need too? Fullerene spool, two pristine nanoforges, and one synchrotron from the core worlds is good for four out of my five worlds. Stealing the items also boosts my income a little (I get more market share) and cripples their fleets if the item stolen is a nanoforge. I call that a win or would if it did not break crises.
Of course, the reward from the League crisis is so lame that if stealing the forge from Kazeron too early perma-averted them, it would be great because then I have HA point gain to get the other crises sooner too. Actually, not a good thing because of big patrol fleets stopping my fleet
in my home system doing patrol scans like with black market suspicion and/or killing trade fleets of their enemies. I should be the one doing patrol scans to them when in my home system!
The Hegemony reward sounds a bit lame, but only because I still cannot use AI cores (in size 4+ worlds) because of the undying zombie Pather cells that I do not want on my colonies. If the Pathers could be neutralized or more easily avoided (that does not involve giving them the planetkiller), then the Hegemony's reward would be more useful. Unfortunately, the Pather reward merely puts them to sleep for a year, same as blowing up a base - totally lame.
Come to think of it, I should start naming my new commander's name Mega Man because the crises have turned Starsector into Capcom's Megaman after I build colonies. I have every incentive to start most of the crises as soon as I can destroy them for their rewards. I do not want to resolve them peacefully if it means giving up income or even simply losing the reward I would get if I just kill them. Only the Pirates give a bigger reward for bribing them (+20% for humoring Kanta instead of +10%). Pathers do not count. I am half-expecting to fight Starsector's equivalent of a Dr. Wily crisis after beating all the crises of every human faction.
Crises come too quickly when my fleet and colonies are weak, but when my fleet is strong enough to kill any human fleet, the crises cannot come fast enough. Next game, I probably will build colonies and keep them at size 3 until I have an endgame fleet, then let my colonies grow and aggravate everyone (except maybe Remnants) for maximum HA gain.