[civilized]

I strongly suspect they sometimes show the ad and credit it for the conversion after the user shows initial interest in some specific product, i.e. when the user was already highly likely to buy before seeing the ad. This would explain why you're often flooded with ads for something after you search for it, go to its website, or purchase something there. (We've all had that experience of buying something and then being tailed by ads for that thing for weeks afterwards, even though no sane person would think we were going to buy that thing again in such a short time frame.)

A story to illustrate: there was once a pizza store that had two guys go out into the city to distribute promotional coupons. The coupons had codes on them so the business could attribute sales to each coupon distributor. John went out into the city and tried his best to drum up new business. Chad stood next to the door of the pizza place and handed a coupon to anyone who was walking in. After a month, 98% of the coupons used were from Chad. Chad got a big bonus and John was let go.