iTunes Match Content Not Showing on new computer

I am subscribed to iTunes Match. I have thousands of songs Matched - a combination of iTunes purchases and my own CDs ripped into iTunes and Matched.

I've got a new MacBook Air. I've set up iTunes with the same Apple ID and authorised the Air against the Apple ID.

The iTunes in the Cloud section of the account page showing on iTunes on the Air shows the Air under Manage Devices and shows my Match subscription.

But "My Music" is empty. I get that I'd have to down items from the cloud onto the Air - but there's nothing listed that I can select to download. My "My Music" page is completely empty just showing the two starting options "Go to the iTunes Store" and "Scan for Media'.

How can I get my Matched content to appear on this computer so I can use it? The whole point of match is being able to access the songs from the cloud, not having copy files across and re-import them. The matched content shows on my Phone without any problems - what do I need to do to make it show up on the new Air?