Were you logged in when you updated. You should have updated from the cloud manager.
Have you subscribed only for Animate/specific products or all CC apps?..Were you already subscribed to Animate CC(2014)? If yes, then after the latest update also the full version should have been activated.
You can check on the 'Help' menu ( along with sign-out option) If the username it displays is your valid CC subscription ID.
I was logged in and updated from the Cloud Manager.
That's what's weird.
I am subscribed for all CC apps, so that's why it is confusing that is just installed as a trial.
Can you try the following?
1) Please go to accounts.adobe.com. Sign in. Under Plans & Products, Are you seeing free membership?
--> If you are using free membership, Animate will be in Trial mode
--> If you are seeing paid membership for all products, then you can use Animate as non-trial version.
2) Try Animate->Help->Sign out. Sign in again with the correct id having subscription.
Sam, did Siva's suggestion work?