Once you log in, Skype will display the status you had when you logged off. If that status was offline, and the users can see you logged in, remove the program from your PC (Control Panel > Uninstall a program) and then download and install its latest version. After that, from the Skype menu select Online Status and then click Offline:
Next, select Sign Out from the Skype drop-down list and then sign in. Now, the users shouldn't be able to see you logged in. If you still have problems, I recommend you contact Skype support team.