Am I reading this right, that the Cosmic Alignment Adventures only happen if the Prelude is included and an Ancient One other than Syzygy is selected?
That is correct.
They probably did this to set it in accordance to the 'side board' system, where the Prelude gives you more incentive than just bringing in the board/the deck. It also allows you to do the adventures.
But if the AO faced is the one that calls in the board/deck, then the adventure is not included.