The Mail rules are being evaluated in your computer, therefore the message has to have been fetched to your computer in order to be evaluated. From there on where it goes or does not go depends on multiple factors:
  1. If the rules, or you, move the message to a folder "On My Mac" that message is deleted from the server and will only exist in the file on your Mac.
  2. If your server is POP3, the message is normally deleted from the server when it is read and will only be visible on the first computer that read the message, ie. it is "On My Mac". There are exceptions to this, but for simplicity I will ignore those for now.
  3. If your email server is IMAP, the message is fetched to the reading computer for processing, but a copy remains on the IMAP server marked as Read. The copy on the reading computer is ephemeral. If the Mail rules move that message to another mailbox on the IMAP server then anyone else accessing that account will see the read message located in the mailbox where the first computer put it. If it is moved to another IMAP mailbox everyone will see the message in this new mailbox, but if it is moved to a mailbox "On My Mac" the message is deleted on the IMAP server and thereafter will only appear On My Mac.
  4. Note there is a rule option to Copy as well as an option to Move, and then things can begin to get complicated/confusing.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein