For that Bill and Caine AU where Bill is a Province of Chaos and Caine is a gaurdian of Order, wouldnt this mean essentially, the people from digital circus arent traumatized from the circus but wierdmageddon? And how did Bill take over earth?
Weirdmageddon took place before C&A shut down which means it was at the same time where Caine consumed the blue Ai. Bill essentially took over earth by having someone build the portal outside of gravity falls. Which also means the humans in TADC were never in the circus. So yes, technically they are traumatised by weirdmageddon instead of from the circus.
In the AU, Bill found the founder of C&A when the company was near bankruptcy. Convincing the founder that he has a way of reviving his business as well as build a supercomputer that can change the world. Important to note that in this AU Stanford never got tricked by Bill due to him still having Stan by his side, so that means Bill had to find other means to build a portal! What better way than trick a company to build the portal for him while also making their project his accomplice?
Since the portal was build outside of the anti-weird barrier of Gravity falls, Bill easily took over the world outside of it.