By default, admins should focus mostly on the activity inside their own instances. Let the behaviour of their users in other instances up to those admins;
This can’t possibly work due to two related reasons:
Small instances don’t have enough moderators to deal with a large number of remote users alone.
Only the threat of losing their main account on the home instance is a deterrent for some users to not troll on remote instances.
I think it should be rather that admins should leave moderation on their own instance mostly to the local community mods and specifically focus on what the users that they are responsible for are doing on remote instances. If admins are unwilling to do that, then this would be grounds for a defederation as this is basically the most important job to build a good reputation of an instance.