This is indeed the adverbconjunction cum "when" (from Old Latin quom), separate from the preposition cum "with" (from Old Latin com). I'm not quite sure why the verbs are passive EDIT: d_e in the comments has pointed out that moveō is generally transitive, so for a sort of "middle voice" meaning, the passive makes sense:
When a bird flies, its wings move.
As you correctly surmised, the nouns would have to be ablative if it were the preposition "with". But cum is also specifically "with" in the sense of accompaniment ("I ate lunch with a friend"), not "with" in the sense of instrument ("I ate lunch with a fork"). So I wouldn't expect to see it used for feet, wings, etc: birds fly using their wings, not alongside their wings.