A change in gravitational potential (because you moved a mass) flows through normal space. It would do the same through the wormhole. So I'm agreeing with you,

A change in gravitational potential (because you moved a mass) flows through normal space. It would do the same through the wormhole. So I'm agreeing with you, and adding how this gravitational slope is created: It's created at the start of the wormhole and changes as you move the mouths of the wormhole, rather than popping into existence at a later time with the two wormhole mouths separated.