I am facing this issue from last 10 days. I am offline (even have disconnected the internet) from all my laptops, desktops and even from my iPhone, still my profile is showing online to my friends in gmail. They are texting me and i am missing it everytime as i am not logged in from anywhere. Firstly i thought my account hacked. After which i changed my password, signed out of all other sessions & kept a two step security verification (Mobile). But still i am facing the same issue. Please help guys....
Are you sure you are logged off from everywhere? Even from your office computer? Double - check whether your phone's Gtalk is signed in or not? As my Gtalk always signs in whenever i turn my cell phone on. This thing might be helpful for you.
May be you have marked that remembered me option on other PC. And when he/she start his/her pc then you get online automatically.
Your cellphone gtalk is still on, you need to kill the service manually. Using two step authentication does nothing to this case. If you are unsure about hackers, look on the lower-right corner of the gmail window and see the login details from all the recent account accesses. Know your gmail/gtalk, don't be a sheep.