I have two IMAP accounts in my Outlook 2013 and neither one of them updates as fast I remember from previous versions. I will always hear my phone's email alert before Outlook shows new mail. It seems like its at least 10-15 minutes later that the email will show up. It's acting as if it were POP3 on a schedule. Isn't IMAP supposed to be almost instant?
When I went to Options -> Advanced -> Send and Receive -> Edit, it has a schedule set for 30 minutes to perform send/receive. Shouldn't IMAP ignore this and ALWAYS be up to date?
POP accounts connect to the server, download the messages, & then disconnect. IMAP accounts maintain the connection to the server, but they still have to perform a "send/receive" action to download the new headers from the server. It's kind of like "push notifications" on a smartphone: if you don't have them enabled, you won't get the pop-up from that particular app.
If you want to get updates sooner in Outlook, change the Send & Receive time to update every 5 minutes.