Private browsing mode doesn't do what you think
Did you think that private browsing mode makes your browsing private? Think again.
Private (or incognito mode) browsing mostly makes it so it doesn't store your history on your computer. Your ISP and websites you hit, including Google, can still track you.
It can still be useful, when, for example, researching a holiday you want to be a surprise to someone who shares the same computer. But you should expect that Google knows you're the one doing it.
More details here.