They don't, you can have multiple people get the same flair at the same time. Most trackers will tell you how many clicks occurred on each reset.

It doesn't always increase by 1, it's just the traffic is quite low right now. In the beginning when it was launched the counter was increasing by around 10 every second, and when it was first entering the 40's, each time it hit 41 it went up by like 5-20 as groups of people were trying to snipe it.

I guess it just listen to the first click and disregard the others