This website also records the last time you've checked in if you look in your profile under "last activity". If you're in a permanently logged in state (as I am), it will show when you open a new browser tab/window.
If you are suspicious that he's checking our SR using your login and raiding your private messages, this is one way to keep track of what's going on. However, this doesn't stop him from lurking the boards anonymously. People have also gone dark for a period of time, then come back under a new name (with new password).
At the very least, change your passwords not only to SR but to your email/FB/ any other place where you're exchanging PMs using another computer off-site if you can. Better play it safe.