The closest I've come to this sort of thing was at Sainsbury's when I used to smoke but wife thought I'd quit by then. I bought a pack and paid using my debit card that I usually use but ii didn't swipe my Nectar Card as you can't get points on cigarettes. Then the exact damn cigarettes popped up on the shopping suggestions in the Sainsbury's online shopping site on my wife's iPad, which my Nectar Card is linked to. I've never used this debit card to pay with for stuff atat Sainsbury online, she always uses her card.
So the only link is the Nectar Card which must somehow be getting my debit card details from Sainsbury's?