For Fujian specifically I would think a handful of aircraft remaining onboard indicates ongoing testing, validation, certification etc. There seems no real reason flying aircraft off to land bases, as there is no need yet for unit rotation, recuperation etc.
Once a carrier and its assigned units are fully operational/in rotational deployment, this dynamic will change. If there is existing infrastructure supporting the carrier air wing nearby (such as in Japan), the aircraft relocate. If they visit foreign ports, or national bases nearby are not equipped to handle the air wing, they will remain onboard.