Is there any more minimal reproduction case here that we can use to test the basic isolations that we expect to see? (Logins are generally held in cookies, for example)
I created a clean Orion RC install, then created a second profile (template being a "Clean Profile"), and then used the two profiles to browse to https://setcookie.net.
I set a cookie in the "new" second profile, and it was not visible when visiting the site from the default (original profile), so there was no "leak" from profile 2 into profile 1.
I then repeated this by setting a cookie in the default profile, and it did not leak into the newly created profile.
Therefore I cannot see any leakage of cookies between profiles, at least in this test.