Amazon customers connect their Facebook friends to find people with wishlists. Someone who has the contact could have information that could link the two accounts, for instance if the OP has someone in their friends' wishlists and they have someone with OP's name in theirs. Or could be connected to a subsidiary like IMDb.

Cookie is a thing.

It's not cookie, it happens across different browsers. It's IP based.

It's probably not cookie-based, or not only cookie-based. Browser fingerprinting and user profiling have gotten very sophisticated, and don't think the big 4.5 aren't using these techniques extensively.

It's probably still cookie based.

If one logged into Amazon in both browsers then it is really just linking to the account (even after logging out).

How could IP-based possibly work for people at places like college campuses?

They take the number of people from the same IP into account. IPs are broken down into public IPs vs private IPs based on traffic/timing of usage etc. There are research papers on this sort of feature contruction using only IPs. Cross device especially uses it extensively to be able to probabilistically ascertain if the person from your house who is checking their phone is the same person who checked smth on the Desktop computer last night based on your online timing, IPs, behaviour over the day. They can figure out, for instance, your office vs home browsing timing, interests etc with the same methods.

Interesting. Do you have the links of these papers so that I can read more?

OP also said they used two completely different browsers

From the same network ? If both browsers are from different computers (worse still from same computer) from same network then the externally visible ip address is the same isn't it ?