Office 365 tenancies are currently being upgraded once it is completed you Exchange, Lync and Admin Portal are in the new 2013 style however your SharePoint environment stays in 2010 mode.
The following walk through will go through the process of upgrading the MyProfile Site Collection from 2010 to 2013 allowing you users use the newsfeed tab at the top in 2013 allowing them to see a consistent view.
My recommendation would be to upgrade this site collection first as it will be used a lot by users and is a key element of the new navigation of Office 365 with Sites, Newsfeed and SkyDrive.
If you are the site collection administrator you will be shown a red bar at the top of the page allowing you upgrade now or later
Here is my current profile site collection
Having clicked Start now you will be taken to a ‘Prepare for takeoff!’ screen allowing you to request a demo upgrade. This will take a day or two but will allow you as the administrator to see what the experience will look like.
Having clicked the Upgrade this Site Collection it will ask you whether you are sure or not
And then its the waiting game to upgrade. You can still cancel it but once the upgrade has got a certain point, you won’t be able to cancel it.
When it has finished it will refresh and give you a small report on the upgrade process.
By clicking on the newsfeed tab you will then be taken to the new 2013 looks and feel My Profile/Newsfeed Site Collection
This article is part of a series of articles on the upgrade process for Office 365 to wave 15