I just came across this accidentally, a friend of mine opened my website on his mobile phone and the website loaded with the admin bar showing me logged in!
This mobile device was using its own GPRS/3G connection and my computer was using my WIFI broadband what I mean is the devices were not even on the same network (except Internet).
I requested some other friends of mine to check the same. My friends were at their home and offices (at different locations in my city) and they all reported that they saw admin bar with ME logged in.
The admin bar was disappeared from the other devices only when I cleared 'all cache' through w3total cache.
On the computer I originally log in, I cannot log out from my WordPress website. When I press ‘log out’, it keeps loading and loading forever. So I just clear the browser cache and think its logged out.
I have been reporting the issue that I could not log out off my websites here --