I’ll have to read it again, but I got the impression he actually participated, not just a fellow on the list.
He was assigned there by the DoD in the summer of 2006 through the summer of 2007 to do research in counter-insurgency and counter-terrorism. thus he was there as a student and researcher and NOT as an instructor. As best I can tell, he was awarded the fellowship after completing his year of research, sort of like I was awarded my MA in history after completing the 2 year program.
From his biography:
McMaster passed command of the 3rd ACR on June 29, 2006, and joined the International Institute for Strategic Studies in London, as a Senior Research Associate with a mandate described as “conduct[ing] research to identify opportunities for improved multi-national cooperation and political-military integration in the areas of counterinsurgency, counter-terrorism, and state building”, and to devise “better tactics to battle terrorism.”[22]
From August 2007 to August 2008, McMaster was part of an “elite team of officers advising U.S. commander” General David Petraeus.
His time as a research fellow at the Hoover Institution in 2003 was part of his Army War College assignment — “In 2003 McMaster completed an Army War College research fellowship at Stanford University’s Hoover Institution.”