I’ve been snooping around and I think you are right. It says what you’ve said in a couple of places.
Eg: on this page, it says “You will need to complete each stage of the Tour within the appropriate 50 hour window in order to earn your Tour Badge.”
Edit: but then I see something else that says you have to “do” the rides “within” the open window. So this would mean you couldn’t start the ride before the window opens and end it after it opens for it to count. Maybe, when I see the official answer somewhere, I will remember for next year when the question gets asked again 