The ad network tracks what you've been looking at but obviously can't actually access your purchases. So all the ad network knows is you've shown intent to buy a tv, not that you've bought a tv.
But it's worth noting that ad networks are more interconnected than most people realize. You can go to Facebook and see the "off-Facebook activity" they have received about you from partners, many of which are retailers. I imagine purchase-history is part of what's shared if you make purchases with those retailers using a email/phone number that's also associated with your Facebook account.