Now, I have created another session to log in through Tor. When I'll log out from here, will I be logged out from the other session as well?
Yes.
If I got your question right, you want to log out of browsing on the other device while logging in on a different device? The easiest thing to do (from my own perspective) would be to change your password on the new device and it will render the other log in inaccessible. It will turn invalid password or username.
The easiest way to do is, logged in only in a private window tab, because when you close the current tab, your current bitcointalk session on that browser will be destroyed without destroying the other session on your other device.