Do you think any sent dislikes from a Lemmy instance would count on that instance? I assume they would, and if the community is also hosted on an instance that supports downvotes then any followers would also receive the downvotes if their instance cares

In my idealistic view, downvotes would be used only for content that doesn't belong in the community, which is also the case where it might be reported and removed by mods. Practically that might not work out, so ¯_(ツ)_/¯