So during Hickman's New Avengers run the Illuminati studied, planed and created a way to destroy alternate Earths during the event of an Incursion. They destroyed several Earths which had previously been vacant of all life thanks to the Black Priests or Mapmakers committing genocide on the planet first. However, when Earth 616 and Earth 4,290,001 were set to collide, the Illuminati were set with an impossible choice. Defeat the Justice League pastiche and destroy their world, to save their own. Or allow the Great Society to win and have their own planet destroyed.
While it was Namor who threw the first punch between the two groups and who would ultimately be the one to trigger the anti-matter bomb placed on Earth 4,290,001. Dr Strange is the one responsible for killing most of the Great Society members, when he released that dark beast creature. Although many of the Illuminati members asserted their intent and held the device to detonate the bomb, none could trigger it and end a world and billions of lives. However, they still built the weapon and it was successfully detonated. How can the Illuminati members justify their actions, especially when none of them were held accountable for it? Sure, Time Runs Out was about Captain America and his Avengers bringing them to justice, but it went nowhere. Time was running out and the cause for Cap and his crew devolved into a feud by the end of it. As Captain America in a power armor died slugging it out against Iron Man while Earth 616 was breaking up around them.