There was a bit of a confusion about the script and also I made a mistake but naming the pivots wrong.
This update should solve this.
Basically now when it says "London Pivot" - it's a pivot that appears during the London session, however it's drawn using values of the previous (Tokyo) session. Similarly - the New York pivot range displays during New York session, however it uses London's High, Low and Close to determine the range.
I hope this update solves the confusion that might have been caused by me not triple checking the code before publishing it.