The only way for them to know you have purchased a product is if you buy it online and get hit with the confirmation tracking pixel on the checkout page.
Most people see ads for a fridge, but then go into a physical store to make and finance the large purchase.
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"
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.
My favorite is when you finally buy something and they still show you ads. Like a coworker mentioned, if I buy a refrigerator I don't need another one... I have one house! Come on! Maybe they do it in case you change your mind? Who knows how these ad companies think.