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Eldritch will take over districts when you take over districts and only then (each district you take is tied to specific districts on the Edlritch side). It's part of the story, and not possible to mess up or miss any content :)

Eg.  Conquering the park will always trigger the Eldritch to conquer the Bar in return, and players can't move to the east side of town until they've conquered the west, so there's no chance of conquering the Bar before the Eldritch get to it.

Hope that helps clear things up!