I'm not sure if this is the correct place to post this question.

Everytime when I log off from Windows Live Messenger, how come my sister and my other friends can still see me online, with the 'Idle/Away' status on?

Even when I'm log on and my status is 'Appear Offline', some of my friends will see that my status is appear as 'Away/Idle'.

HOw can I fix this problem?

Never heard of that before try go for the simple option and uninstall and reinstall or update to latest version and btw when you exit do you right click green man in in task tray and click exit?

Are you sure you are exiting messenger and not just closing your list pain?

If you are using messenger plus it is a buggy little monster.

Try a uninstall of messenger and a reinstall.