The story wold work better with the Predictor monitoring your brain "in real time" and seeing your intention to push the button form before you are aware of it
That's how I pictured the Predictor working, myself, in an attempt to justify the mysterious factor that sets my reaction time to exactly 1 second (and possibly also to keep in line with the determinist theme.)
If it's worth saying, but not worth its own post, even in Discussion, it goes here.