That's a good question. Private windows share a single cookie jar among the private tabs. Is it possible that the Southwest site uses third party cookies from any sites you were logged into in another private window tab at the time?

Hmm, also, how did you originally load that Southwest page? If it was from a promotional link, that usually connects the request with the promotion (whether that was a particular website, or as specific as an email sent you at 10am Tuesday). If you want to visit a site without any trail, make sure to navigate directly through the address bar or a general bookmark, and not using a link.

Thanks! Yes, I did navigate to Southwest from a promotional email. Will open a new tab and go directly next time.