I am away from my car at the moment, but I don't recall anything that would resemble white, plastic or cups in the locking mechanism on the top or at the window.
They go in the top part of the windshield side clamp. Another thing could be is a shrunk header seal that allows it to get closer to the windshield frame causing excessive gap. I did have to adjust mine out 3 turns when I test fit my new seal Vs the old one (or what was left of it)