By default, iPhone will only push “Inbox” from your Simplifying IT Exchange email account. This is definitely uncomfortable, especially if you use server rules to organize our mailbox.
Making iPhone to push additional folders is simple:
Settings → Mail, Contacts and Calendars → Select your MS Exchange account → Mail folders to push.
From now on, iPhone will push those additional folders for you. Unfortunately, the notifications are not satisfactory: there will be sound notification each time new message is pushed, but no badge indicator appears on mail application icon unless the message is pushed into “Inbox”.