Mac mail moves deleted messages to different server

I have a business email account (imap) that I use with Mac Mail. I also have a Gmail account. I had been noticing (for a while now) that deleted messages from the business account never seemed to go to that trash folder. I couldn't find them, so I assumed that they were being deleted immediately. Today, I realized that they are my Gmail (All mail) folder. It seems as though they are being moved from one account to the other.

To be clear, I am certain that they are being sent from the business account, not Gmail.