Federation doesn't mean anything like that per se, you're talking detail of a particular implementation (I assume Mastodon but what do I know).
Federation just means multiple independent servers/domains can talk to each other, such as with email or Matrix, without the need for central authority (other than for discovering each other).
The concept that you get wrong is that nobody mirrors content. Servers receive the content from the one of the original content creator, if they exist in its recipients list. Public content usually is distributed to all servers that the original server knows about. However it's always a PUSH of the content.
Federation just means multiple independent servers/domains can talk to each other, such as with email or Matrix, without the need for central authority (other than for discovering each other).