I'm not sure what you are saying in your last post actually.
I'm not sure what is going on then. It works for me as expected. When I select "Close All" it closes all of the open tabs from the private session that just ended. My Safari opens to a blank white page with an untitled tab.
Have you tried closing Safari completely, restart the iPad and then try again? Or have you tried resetting the iPad?
Go to the home screen first by tapping the home button. Quit/close open apps by double tapping the home button and the task bar will appear with all of you recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner to close the apps. Restart the iPad. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.