I will share you my personal experience here. I usually log in bitcointalk on my laptop. Once i logged in through my mobile chrome browser as i need to check some thing important. I then logged out from my mobile browser. Later when i reached to my laptop i came to know that my account was logged out on my laptop too and i had to login again.
Remember that i logged on one in my laptop and it kept login in forever unless i logout out myself. So as per my experience, if you log out your bitcointalk anywhere, it will logout you out on all the open sessions.