All of the powers, privileges, immunities and rights, exemptions from laws, ordinances and rules, all pension, relief, disability, workers’ compensation and other benefits which apply to the activity of officers, agents or employees of the State or the county or any public body when performing their respective functions within the territorial limits of the respective public agencies apply to them to the same degree and extent while engaged in the performance of any of their functions and duties extraterritorially hereunder, and while engaged in the performance of any of their functions and duties under any contract or agreement authorized hereunder.