what does downloading messages mean in mail app

Log into the Web Portal of your e-mail server using the Web Browser of your choice.

Are the messages still appearing on the Web Portal ?

From your earlier description, it seems the Mail Account is using IMAP Protocol

Using that configuration would mean, what is appearing from the Web Portal would be reflected back into the Mail application

You can Delete the Offending message on the Web Portal of the account

That should stop the " regurgitated " messages from re-appearing

It means it is retrieving message from the email server, saving them on your Mac.

Did you rebuild the mailbox? That would cause it to download all the messages available on the server. Otherwise, I don’t know what is happening.