I honestly don't know for sure. Maybe it's cached on whatever instance your using, or maybe your instance is pulling the content directly from the target instance's database (or more likely an API-like ActivityPub request to the target instance).
I was under the impression that lemmy/fediverse essentially functions like email. Your messages and content are stored on your server, but you can communicate with anyone on other servers.
I meant harm in that it affects "one or a few students" rather than affecting "practically all students."