So, when you post to a community, you're posting to the local copy of it. Your host then forwards that post to the site that houses the community. When you're banned from a remote site, nothing interferes with this process until the local host forwards things along. By that time, you've already posted.

Now, the site that's housing the community is responsible for federating content it receives back out again, so while you can continue to post to the community locally, those posts won't make it to any other copy of the community. But because each instance's copy of the community is quasi-independent from each other, you can, IIRC, still engage with other local users in that space.

Fake bans aren't a thing, but banning from an instance doesn't necessarily ban them from all communities (just the ones they've interact with up to the time of the ban).

This means someone on instance B, who is banned from instance A, can still interact with communities on instance A via instance B if instance B was not informed the person was banned from the community.

However, a user from instance B, banned from instance A, interacting with a community on instance A via instance B will not have their content federated via instance A (the home instance of the community). Thus, only other users on instance B should be able to see that user's submissions.

Clear as mud?

Edit: Maybe I can clear it up with an example.

Let's say you and your friend are both on lemmy.cafe. I see your friend around in the Lemmyverse from my instance, and they're violating a bunch of my local rules to the point they merit a ban. Your friend has not interacted directly with any communities on my instance, so when I ban them, no community bans are federated.

You and your friend are both subscribed to, say, !30rock@dubvee.org. Even though your friend is banned from my instance, they can still post/comment there from lemmy.cafe since that instance has no idea they're banned from mine; non-local bans aren't federated, and since they hadn't interacted with that community prior to me banning them, no community bans were sent out.

However, none of the posts/comments they make to lemmy.cafe's local copy of that community will be federated by my instance (where the 30 Rock community lives). Thus, only users on lemmy.cafe can see what the banned user has posted.

Put simply, Lets say hypothetically he's like you on lemmy.cafe.

and we'll say he's posting to to lemmy.world/c/memes which he was banned from.

His post will show up to lemmy.cafe users connected to memes... but his posts will only show up on the lemmy.cafe version of memes. When cafe federates back to world, world will just ignore the posts and not share them.

In addition they won't be seen by, lets say programming.dev here, while it hasn't banned this person, it's looking to world for it's copy of the community, which will not have your friends posts.

On lemmy, a ban can be a few different things:

1. Banned from the instance your account is on. This means you have to make a new account, usually on a different instance.
2. Banned from a different instance than the one your account is on. This means you get banned from communities you’ve participated in on that instance, and that instance will no longer federate with your account. You might participate in new communities on that instance, and people ~~not on that instance~~ on your instance will see your comments, but people on the instance you were banned from and other instances won’t see them. From the perspective of that instance you don’t exist anymore.
3. Not banned from any instances, but banned from individual communities. You can’t post in that specific community but can still interact with the instance that community is on.

Like someone else said, clear as mud, lol.

Go to a comment you think shows he's "fake banned" from.

Then go look at it from that instance instead of a 3rd party instance.

Their comments won't show there, so they won't get any engagement from people viewing from that instance.

Because they're making the comments on that 3rd party's copy, but it doesn't federate to the main one that they're banned from