As an Amazon seller, I can confirm that they have tracking linked to each seller. Their system does this via their FNSKU (fullfillment network stock keeping unit) and that is unique to each seller for each product. So if I want to sell a product, that product has an ASIN that defines it specifically and then any seller in the Amazon system that wants to sell that product needs their own FNSKU that applies only to that ASIN. Those FNSKUs are tagged on the items. If you've ever bought third party stuff on Amazon, the numbers are also 10 digits long just like ASINs but they usually begin with an X. FNSKUs can also match the ASIN and that is usually given to the seller that creates the listing so that seller has FNSKU=ASIN. So if you buy private label stuff that is their own branded stuff that no one else sells, it just looks like the ASIN and you probably ignored it. But if you buy a big brand name product like Nintendo, Star Wars, or anything with multiple sellers that sell via FBA/prime, you'll probably see the FNSKU beginning with X.
EDIT - in case it wasn't obvious, Amazon uses the FNSKU barcode for fullfilling their orders. They might have 10 sellers with the same ASIN in that specific warehouse, so the Amazon employees fullfill via FNSKU in those cases, which is why they would require the FBA/prime items in their warehouse to be tagged with the FNSKU to identify which seller owns that exact item vs all the others that also have stock in that warehouse and perhaps even in that exact same shelf/bin.