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.
That's my understanding of it, I'm not an expert so.. I'm only giving 70% confidence in my answer.