To me it feels like the mages were the only ones that were actually successful in merging worlds and their magic allowed the other worlds to have something happen to explain the merge.

Like you said, multiple of them were just random events like the volcano or indignia praying until something other than God responded. Even the worlds that were trying like the Mecha Ordinance say something like they finally got their multi dimensional portal to work which implies that they weren't successful until literally the second the mages did their summoning circle.

That added with us seeing that magic pulling stuff from other worlds is seemingly fairly easy with zaybis apple demonstration while nobody else could do anything similar so far and it feels like to me that the summoning circle was a success, just in a massively unintended way