Good news. I found a page with a YouTube video where a cute Filipino girl with a red bow in her hair and a giant heart pendant demonstrates how to use this gizmo.

http://mizcozmeticfreak.blogspot.com/2010/04/soft-contact-lens-inserterremover.html

You're right about the cup being used to insert the lens and the tweezers to pluck them out. It looks like the girl who is demonstrating this device needs a little more practice, though. She seems to flinch a lot.