IIUC, you can do attribution with a very basic ad: <a href="website.com/ad-34" ping="fb.com/my-product/ad-34/ping"><img src="fb.com/my-product/ad-34/img.jpeg" /> Come buy my product, you'll love it!</a>
Then you sum up all the "/ad-34" hits, and figure out how many of those user sessions (which are now on your own site -- single domain, but perhaps leveraging a script supplied by the ad network) went and actually bought something. The ad network can correlate those sessions with the "ping" it receives to determine clicks vs. conversions.