Oh no, that doesn't matter. I can search for something a buy it online, and be pestered with ads for the same product for days.
The ad-placement folks have technology and patents and millions tied up in all that. And what do they come up with? "Show ads for what they just bought"
Its more complicated than that. You are probably included in separate funnels that can't communicate.
The "fridge store" is doing a pixel based retargeting list, which is easy to take you off when the purchase is made.
But they also might have a list of 'customers likely to purchase a fridge' from Google searches that you are being served ads to as well. You might be on a 'look-a-like' list from Facebook, because people in your demographic tend to buy new fridges. You could be removed from that list if Google shared the IP addresses of everyone on their list, but at a serious cost to your privacy. These walled gardens are ultimately good, but result in a ton of advertising inefficacy.
I know its annoying but the advertisers are smart enough... we don't actually want them getting any better than they are now.
The ad-placement folks have technology and patents and millions tied up in all that. And what do they come up with? "Show ads for what they just bought"