[masraum]

In addition to your browser possibly providing more info that you'd want (which seems odd in "private" mode). You could also try another browser. Websites can only get information from your PC that is allowed by the browser. It's possible that safari is allowing more than you would expect in Private mode. Maybe try FF or Chrome (also in their respective private modes).

I think it's also possible that your gmail account may be a give away. You might try firing up your VPN and creating a new gmail account over your vpn. Then use that account when you go to the website.