ACF cannot be updated normally in WP when it is included as part of a theme. ACF uses the WP system for updating plugins and this cannot be done if ACF is not installed like any other plugin. In order for the client to update ACF you must manually update your version of the theme and provide during a theme update.
This is one of the issues with including any plugin as part of a theme rather than installed as any other plugin and is one of the reasons that many themes now have dependent plugins and install those plugins into the WP plugins folder.
