You can register a TileDB array that is already created in a cloud bucket under your control, either via the TileDB Cloud API, or in the TileDB Cloud console as follows. Make sure that you have already set up your AWS credentials, which are needed to access the array you are registering, as those will have to be selected in the drop down list in the pop up, after you click on the "add array" button in Assets -> Arrays. You can also choose who will be the owner of the array (you or an organization you belong to). Your array will be accessible by tiledb://<namespace>/<array-name> after it is registered, where namespace is the owner of the array and <array-name> is the name of the array that you can select during this registration process in the pop up.
There is absolutely no data movement upon registering an array with TileDB Cloud. Your data continues to remain in your bucket and you are the full owner of this data. TileDB Cloud just records the path and the AWS keys that can access it, so that it can govern access when you or the users you share this array with need to access it.