I believe that you might need (on the x1) to check in the updates section of your games and apps. Just in case, if you're running instant on though, it'll update.
I had deleted the Closed Beta, so when I downloaded it -- it was renamed the Open Beta.
Monday morning my Xbone One automatically updated from Closed beta to Open beta. Ran the game to check if it was lying to me, new welcome intro video from Ubisoft and a countdown timer to the open beta appeared.