This is old info and may no longer be applicable since we've gone through a few upgrades, but here's what I was told:

12/7/2024 3:05 PM welcome.

it's fairly straightforward once you know how it works. reports always go to up to three different instances:
reporters instance
community instance
reported users instance

on each instance, all instance admins as well as moderators of said community can see and act on reports. if an admin takes action against a post, this will only federate if the community is on that instance, as they don't have authority further than that (unless they're also community mod).

this unfortunately can also lead to a remote moderator thinking that a post has already been removed when in fact that's only the case for their local instance.

as admins can also resolve reports, this can also lead to remote moderators missing reports if they're resolved by the time they'd see them. i'm not sure how other instances deal with this, i imagine that this would mostly happen in cases where admins think "remote community - unlikely to have local mods that'd look at this".

report resolution however does not federate, so if a remote moderator acts on a report the report will still show as unresolved on other instances that received it. as far as i know the only thing that currently resolves a report with federation is removing the associated post/comment, as that triggers relevant code to mark the report as resolved. removing content by issuing a ban that also removed content will not currently resolve reports.

the general takeaway from this is that the only reliable way to receive reports in a community is still to have an alt on the community instance.