A Good Question Bill.
It goes off your race at the time you touch the end portal in the temple.
So for example, if you are a Harakim on lab 8 at Sgt major and touch it and you are the fastest Harakim then you become the Champion Harakim at the end of the quest.
To become the Champion Arch Harakim you will have to be on Lab 13 (well past Lab
and it will take you considerably longer to get there but if you are the fastest then you become the champion Arch Harakim.
Same goes for Seyan, you will have gone to lab 13 and back again to private and up to Lab 7 again. The total time online when you hit the end portal in the temple and your race at that time is what counts.
Times for arch races will be considerably longer than non arch races.
Caution: If you touch the end portal in the temple b4 you have completed the quest requirements then there is no way to undo this.