Their addon seems to have some more problems, took me several frustrating hours now. Solution is:
Deactivate their ACF Field Addon and simply add the field names in the custom field section instead of mapping them with the acf groups directly. And also remember to change the fields, that should get updated on each import (switch from acf to normal custom fields and add the field names).
This will also work with fields, that are created via json.
Thread can be closed then. Thanks!
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