Why did a gift file remain on our computer after I closed Incognito?

My partner asked what “engraving-proof.pdf” was doing in Downloads. I had ordered her present in Chrome Incognito and closed the windows afterwards. I thought the whole shopping session would disappear.

The file was a preview I downloaded from the seller. The surprise is now partly gone, but the seller did nothing wrong and my partner was not snooping.

What should I remember next time? I want a realistic way to keep a birthday purchase private on our shared computer, rather than treating the private-window icon as a magic eraser.