Does Firefox private browsing still work?

A few months ago I logged out of Facebook and cleared out all known Facebook cookies from Chrome. Then I moved my Facebook account to a separate account container within Firefox. Use that container for FB and FB only. And I never access FB from Chrome. Yet somehow ads relevant to very specific searches I did on Chrome still appear on FB. Can someone explain how this is happening?

P.S. On my mobile phone, I never installed FB app, and I use Firefox Focus as my default browser.