My understanding is that the FEs awaken once someone gets the Alpha reactor. Generally what happens is they'll demand the technology for various reasons related to their empire type (the Materialist/Xenophiles cite some BS sounding law that makes modifying the Enigmatic Reactor illegal for "lesser" empires, for instance) and the person they're confronting will either give them the Alpha Reactor designs or defy them. In the case of the former the FE will awaken with Alpha tech, in the latter the FE will awaken and declare a War in Hell on the target empire, where it ends with either the FE being wiped out or the upstart being crushed and their tech taken.

Of course, there's nothing preventing each FE from issuing the ultimatum in succession, so past a certain point it becomes dangerous since your ability to kill each FE before this point (or as they try to steal your tech) becomes important to ensure you don't get swarmed by multiple deathstacks.

ohh, ok. Then I have to disable the option to get alpha tech then

i wish we could disable that feature, and just stick to them awakening after endgame starts

It sucks when you've been avoiding to get that tech but the AI gets it and awakens in mid game when noone can deal with the buffed FE ships