Lieutenant Colonel Fellini was the duty officer of the Air Force Air Police at the time they captured Captain Kirk. Fellini was a seasoned Air Force officer with many years of service, a veteran of the Second World War, and a recepient of several high Air Force decorations. Fellini was also a very stern and by-the-book officer and could not understand how Kirk had infilitrated a top secret Air Force base and became infuriated at Kirk's very bemused attitude towards the entire situation.
During an inadvertent incursion to 1969, the USS Enterprise was approached by an aircraft. Images of it were caught by the aircraft's wing cameras, and a description of the encounter was recorded by flight control of the 498th Air Base.
After destroying the aircraft, Kirk ordered the pilot, Captain John Christopher, beamed aboard. This created a potential conflict, as Christopher's as yet unborn son Shaun would be a vital part of the timeline that ultimately led to the Federation. Forced with a need to return Christopher, Kirk visited the air base to recover the taped and filmed evidence. He succeeded in this, but tripped a silent alarm, drawing the attention of the air police, including Fellini. Kirk distracted the air police long enough for Sulu, his partner in crime, to escape.
Fellini questioned Kirk at length, without learning much, before Spock beamed down and rescued Kirk.