It works like this:

Essentially when you view his post on lemmy.one while logged into lemmy.world, you are not actually viewing the post on lemmy.one but a cached copy of the post on lemmy.world.

Lemmy.world allows downvotes so you click the button. It updates the cached copy on lemmy.world with your downvote and then send an update over to lemmy.one telling it about the downvote and to please do the same to keep the original post in sync with the copy. Lemmy.one ignores this update and chooses to retain the original based on its rules.