The same happened to me but its completely reasonable to expect this in my case, I was most certainly tracked by searches pertaining to vehicles as I was shopping around. The actual purchase I would imagine should NOT show up in the same datasets as it should instead be limited to the companies that were actually involved in the purchase. Given that the purchase of a new vehicle is significant enough that folks might put effort over a period of time evaluating vehicles, it makes sense that ad folks who see these analytics would roll the dice and hope to hit me up as its statistically likely that I have not immediately purchased a vehicle within such a narrow timeframe relative to initiating my web searches regarding this purchase.
Yeppers. It would not be in the same dataset for sure. We have no idea you made the purchase. We just know you searched for it.
Even if you did make a purchase for a brand and the advertiser knew you made the purchase, it doesn't mean the brand has more than one advertiser working with them, where you still get ads for that brand when you know THEY know you made the purchase. They just may have 2 advertisement companies handling different channels of marketing and not talking to one another on who purchased (i.e.: social media advertising versus Google search).