The registration of ADE (digital editions) with an AdobeID gives you the capability to read books that are associated with that ID.
It does not automatically make the books available on the computer/device.
There is no 'cloud' version of your books maintained by Adobe or by the book vendors.
You must manually copy the books from one device/computer to another.
For that reason, it is also important to keep a backup of any books you value, along with your backup of other important documents etc.