I tried the same thing on Windows with Google Chrome(Uses Webkit) with Delicious.com in browser i logged in with my gmail account and in AIR App I logged in using yahoo ID. I can still use my chrome session.
tomorrow I will check on Mac OS and get back to you.
meanwhile can check if this is happening with all the sites using Sessions?
Also, can you check if you can reproduce the issue with Chrome on Mac? (Chrome-AIR and Chrome-Safari)
Currently I can not check suggested scenarios on Mac. But I have observed it with other sites too (it's not only Delicious.com related). I noticed this problem very often with sites using GoogleID or YahooID. For instance: I was logged in to GMail, then I run the AIR application which use another credentials (fake account for testing purposes). After succesfull login in AIR application the account in GMail was also changed to the fake one.