"I deputized him" what does this mean? Criminal mids?

County sheriffs have the power to deputize civilians in situations where enough trained officers aren't available, though their law enforcement authority is usually temporary and more limited in scope and area. It's supposed to be voluntary and there is no written law that says a civilian MUST assist the police (except as a witness during an investigation), but throughout history during dire emergencies it has not been unknown for people to be forcibly conscripted into joining and aiding the authorities. In any case, civilians already have the power of citizen's arrest and the right to use deadly force to protect others, so that ex-special forces guy may not have even needed to be deputized in order to be allowed to stop a suspect.

Well, first off that is TV and not quite the way it works.

A sheriff is an elected official and hires deputies at his own discretion. A sheriff can make little deputies but a police officer does NOT have this capability.

An officer can request assistance from citizens and I believe you are obligated to assist.