I'm not sure if you ever got your answer, but I linked my primary Xbox account to a newly created PC account so that I could cross-trade. As I'm writing this, when I logged into my account on PC everything transferred beautifully and I have successfully cross-traded. As far as being auto-logged into your PC account on the website, I'm noticing that too, but I can still access my account with my Xbox credentials if I want to sign in that way.