Peeking into the source:

  /**
   * Detects incognito/private mode in various browsers.
   *
   * Adapted from:
   *   https://gist.github.com/cou929/7973956
   */

Link for the lazy.

https://gist.github.com/cou929/7973956

My guess is that they feature detect, using disabled stuff (eg localStorage error 22 on safari private mode) to find out if your browser looks like one in private mode.

There are certain browser APIs disabled in the browser in incognito mode that can be detected. How else would you implement incognito mode?

By sandboxing, e.g. localStorage fully functional but deleted at the end of the session...

Mozilla recently released containerized tabs[0], I imagine the next logic step is building containerized Private Browsing Mode

[0]: https://addons.mozilla.org/en-US/firefox/addon/multi-account...

My understanding is that things actually went the other way. Private browsing came first, then the same approach was used to create more labels than just "private" and not "private". I think more features may be turned off in private browsing mode though.

I use multiple computers daily and not having those synced with my Firefox account is a pain in the ass.

That's interesting. Why are the storage APIs disabled, instead of just using ephemeral storage that goes away when the window is cleared?

It's less work to disable them. There's likely already an API access control system in place, for internal-only APIs, testing, etc.

It also means sites can avoid promising to do things that aren't actually possible, like saving information for access next time.