Google Chromes private incognito browsing will not keep a track of the website on the local computer, but remember the details are all on their server. So in case, somebody wants to know the details, he will make a request to the service provider. The safest bet is used to a VPN on your own personal device over data and not on your company network to keep your browsing private from your employer. Use browser security tools such as HTTPS to protect your data even when you’re not browsing privately.”]
Source: https://hackercombat.com/is-private-browsing-on-incognito-secure/