In order to use premium on the Xbone after transfer go into the BF4 in game store to the premium section, repurchase Premium for zero dollars, quit BF4, all premium to download and install, then restart BF4 so the game initialized with your premium file present on the console's HDD.
After BF4 is started go back to the BF4 in game store to the premium section and download all of the expansions present. Quite BF4 and then go to games and apps and after the expansions are downloaded install them. After all expansions are installed start BF4, go to multiplayer, then server browser and set up your server browser filter with all of the games and game modes that you wish to play from the expansion packs.
Regarding Xbone asking for a credit card for that transaction, you might want to ask Xbox Live customer service about that since free content should not require a credit card to be active on your account. You contact Xbox Live Customer support here: support.xbox.com/contact-us