When I right-click on the my KDE desktop and select 'Configure Desktop', I see a Screensaver option in the left panel. If I click on it, I have a checkbox that says 'Start automatically'. If I don't have that checked, then it doesn't start.
If I do have it checked, then underneath that checkbox is a 'Require password to stop' checkbox. If I check that, then I have the problems that you're having - I need a password to log back in.
This link might not work, but I'm going to plunk in a link to a screeshot. Does yours look the same way?
http://farm1.static.flickr.com/151/3...ee0577b2_o.png