Earthlink Mail Problem

I currently have an Earthlink email account and access it form my iMac, Mac Book and now my iPhone via Mac Mail. The problem is that if I access my email, read and delete the messages for one of the computers (such as the Mac Book) all is fine. However, when I login for my iMac all those message start to download again. Some of these messages are several months old. My new iPhone is now trying to download 200+ old message from Earthlink.

How do I permanently delete email from Earthlink?

Thanks
Mike