You are quite wrong. If they were under contract - a very large contract, no doubt - to the US government and the president or secretary of state told their employer (a government contractor) to get rid of them, they’re gone. Given their backgrounds, however, it’s very likely that Paronto and his associates were individual contractors to the CIA, which makes it much easier to get rid of them.
The supposed “full and open”, squeaky clean government acquisition process represented by the Federal Acquisition Regulations (FAR) and DFAR is a total myth. But that’s another subject...
Nope. I am a contractor working in the IC after having served on active duty for 20+ years. POTUS has no authority to fire contractors. He can terminate a contract, but not an employee that is not in his employ. Pressure from POTUS or SecState notwithstanding, there is no direct method for the top Executive to do so.