A person in the US sending intelligence to a foreign government would be monitored and investigated by the FBI, not the CIA. The CIA's job is to spy on other countries. Preventing espionage within US territory is the job of the FBI's Counterintelligence Division.
Upon arrival in Rome, Cassie is seen exiting the aircraft and entering the gate/boarding area. When arriving from the United States into Italy all passengers and crew would be required to deplane and proceed through the customs arrival hall. Internationally arriving passengers and crew would be prohibited from exiting into the gate area as Cassie did.