The Secretary of Finance may make such requirements as will tend to safeguard or systematize the expenditure of the State's money; but the Secretary of Finance shall make no requirement that will unnecessarily interfere with the prompt payment of the amounts due, and under no circumstances shall the Secretary of Finance cause the payment of salaries of state officers to be delayed beyond the date upon which the same are due, nor shall the Secretary of Finance have the authority to countersign the checks of the Treasury Department.