IMAP Downloads Old Emails?

I use Mail on my MacBook Pro, iPhone and iPad to manage my website's email server. I've noticed recently that, no matter how many times I move emails to folders or delete the messages, if I click out of the inbox, when I click back, all the emails are back. Hundreds of junk email messages, back where they were after hours of deleting things. It happens on all devices.

My mail is DEFINITELY set to IMAP, and it's happened more than once. Does anyone have any insight?