It's not a problem. It's taken care of.
Your dad doesn't know what he's talking about.
An incognito search is when you browse without identifying information. My company does them constantly, so we can see how ads are performing online and what those ads look like to people outside the company.
If you have the Chrome browser, go to the upper right corner and IIRC you right click on horizontal lines. I am on my phone so I am unsure. Same with other browsers.
You can Google how to do an incognito search, and then erase your browser history if for some reason you don't want your folks to know that you did that.
At some point, you need to assert a right to privacy. Yes, even if you live with them and they pay 100% of the bills. After all, you close the door when you go to the bathroom, right? Same principle.
You're allowed to spend time on your own without them hovering, full stop.