A contractor can maintain their jets however they want as long as it's safe and they can meet their contract requirements. The contract maintainers can stay at their job as long as they want. The USN and USAF maintainers move every few years and have pretty good retirement benefits (which used to be better but are still better than what most private companies give), and have to get lots of additional training and all that needs to be paid for. A contractor is still supposed to follow all the safety regulations, but contractors seem to be able to generate sorties at rates that military units couldn't manage even with double the manpower.
Contractor pilots are paid strictly to fly. Naval aviators and USAF pilots are both subject to "up or out" policies, where officers that aren't promoted are told to leave. This means military pilots have to serve as staff officers to keep themselves promotable. During a staff tour they either quit flying or they fly less, which kind of wastes the money spent on training them. There are good reasons for requiring this (and some good arguments against it), but the bottom line is that contractors don't have to worry about it and can operate cheaper because they aren't wasting 20% of their personnel budget with a fighter pilot working behind a desk.