This seems, to me, like an opinionated default that start9 considers good security, (or maybe certain apps do) since privacy mode disallows cookies and other things that show where you have been. Therefore, I'd expect the answer lies that way more so than at a browser level.

edited to add their mission statement: Mission -- To eliminate the need for trusted third parties in the human/computer relationship. https://start9.com/about/

That sounds like what privacy mode would try to do.