Private mode can leak logins

I have seen that sometimes logins can be leaked from regular mode into the private one. It is easy to test using Google. Login into Google in regular mode, switch to private and try to search for something . Sometimes, not 100% but frequent, you will get private mode with your google login from the regular one. And it is not that this is some glitch, you could check in Google activity log that the searches are logged.

Not sure why it happens, as we do set offTheRecord for private tabs. I'll look into it and will update here. Any ideas on checks are welcome.