Was this during the same browser session or did you close down the first Private session and then open a completely new session/browser instance? Was tracking blocked? AFAICT, Private Browsing will use cache while the session remains open, otherwise sites requiring continuity of information would not work properly. Standard operating procedure would be to then dump the cookies, cache, and history when the session closes.

If this was related and not a freak coincidence (which means it should be repeatable; test with fresh cache, no cookies, different IP), the only way for the data to be relayed would be if cookies and cache were retained from earlier/simultaneous browsing. If you frequently look at planes and motorcycles, cache from even earlier sessions in the past may be detected.

Logging into an account is not required for tracking to occur; pages can deposit cookies and other identifiable files that other pages and websites can check for without the user identifying themselves.

if I open a new tab after closing the the initial tab this occurs. If I close and open a new Firefox window it does go back to the default youtube screen (no recommended screens).

I guess it is normal for the original open firefox tab window to maintain previous closed tab information in the same Firefox window. When firefox is closed and re-opened all information is removed.

Okay, thanks for testing and reporting back!