How to set up Outlook.com sync in iOS 6

Adding Outlook.com as a mail account works fine on my iPhone 5, but it doesn't sync with the desktop or mobile web sites. For example, if I delete mail from my iPhone, it is not deleted when I check for mail in the browser. I think this is because iOS sets up Outlook.com accounts as Hotmail by default, forcing it to use POP3 instead of Exchange. The problem is, when I set up my account as Exchange, it gets automatically changed to Hotmail without asking me. Does anyone know how to force iOS to set it up as an Exchange account?

P.S. Outlook.com Exchange setup worked fine on my old iPod touch running iOS 5.