How do I setup my imap client so that if I delete a message on one client, it deletes

I have my iPhone, iPad, and Mac setup to retrieve my email. I have all clients setup as IMAP. I want to be able to open email on one device, delete messages I don't want, read others, and have both actions reflected on all devices. What setting am I missing? I have another email (from a different company) which works as I want it to, but I cannot see any difference in my settings between accounts. Any ideas?