He was working for Onrac, you are correct. None the less, it was Lufenian technology being used. Technology I kinda doubt the people of Onrac fully understood, which may explain why everything went so far off the rails.
The game explicitly refers to Cosmos as being weaker than Cid's wife. Bear in mind that Lufenians were immensely powerful because of their technology, so much so that one from a less advanced civilization wouldn't be out of place mistaking them for gods. Most of them also had a latent talent for magic that bordered on the insane. Suffice it to say, Cosmos's ability to placate Chaos at all was due almost entirely to her resemblance to that woman. Doubt she'd been near as effective without that edge. After all, Chaos loved his momma.
At any rate, to note, I was not implying Cid's wife could control Chaos through sheer power. Neither of them could. He obeyed them out of sheer love. What I am saying is that Cosmos did not possess sufficient power to subdued him through direct means, although the people of Onrac did try to imbue her with that kind of strength.