Hello Floyd,
Please inspect the following article, I think your problem may be that the "leave a copy of messages on the server" checkbox may be checked, which would result in emails being downloaded every time Outlook starts up. I'm not sure how this behaviour works when only accessing email using the same client, but I imagine it could cause the issue you are encountering.
https://support.office.com/en-gb/art...6-17f6139bd9d1
Let me know if this doesn't help and I will continue exploring possibilities.