I don't see the issue here
Also, your account is yours to protect - if someone hijacks it or guesses the password, or you leave the browser open (or cookies/passwords remembered) on a shared or public computer, and they do bad things in your name, that's your problem and not ours

Change your password and keep it safe if you believe that could be the problem, and watch the browser settings if you're not the only user of the computer.
Also, the grey/yellow bird (chocobo) is an online indicator - grey for when you're not logged in and yellow when you are, so don't worry too much over that one
