Start from here:
Get Stats, Coaching Records, Team Ranks, Coordinators, and more for Sean Payton on Pro-football-reference.com.
www.pro-football-reference.com
Go to full coaching history.
You'll see that Payton broke into the NFL coaching rank with the Eagles, where Gruden and Callahan were already employed.
Payton learned the WCO there.
Look at the Eagles team page, it tells you the offensive scheme a team run.
Next, go to the Giants team page.
When Payton arrived there, Jim Fassell was already the HC for two years, and he was running the WCO.
That was why Payton got his new gig.
You just confused yourself by assuming that Parcells was with the Giants then.