There was indeed a bug here, and partly thanks to the investigation of @Arkshine, it was relatively easy to fix:
https://github.com/discourse/discourse-data-explorer/pull/363
This has been merged already, so once your site has been deployed you should be unblocked @ganncamp.
If I understand correctly, you want an automation that is a one-to-one mapping between a group and its report? (I.e. group_a receives a report with group_a data, etc.)
There is (currently) no connection between the recipient list and the report parameters, so to accomplish that you’d need to set up one automation per group. In this case you might want to change the parameter to group_id.