Roughly: both the samples are in both world A (up/down) and world B(down/up), and when you interact with them, you get split and are pulled into both world A and world B, and each copy of you when you interact pulls the thing you interact with also into A and B, and so when you compare results, the A-you compares the A-result and the B-you compares the B-result.
The splitting is not immediate or faster than light. But it moves at exactly the speed of information, so you can't race ahead of it and watch it happen. To interact with it is to become part of it.