One of the main features I love about Safari is that in private browsing mode, the tabs (at least) appear to be completely isolated.
If I go to Facebook and login in one tab, then open a second tab and go Facebook, it doesn't recognize that I have logged in. There's moments where that is annoying but most of the time it's useful.
Yeah they are, which is IMO a good thing but it'd be better if you could link them somehow, maybe have a temporary session or something.