A director for each of the above departments shall be appointed by the city manager and shall serve until removed by the city manager, or until his successor is appointed and has qualified; provided, that the city manager shall assume the directorship of the department of finance, unless otherwise ordered by the council. Each director shall have power to prescribe rules and regulations, not inconsistent with this Charter or ordinance, for the conduct of his department and the preservation of the records and property under his control. Subject to the control and supervision of the city manager in all matters, the director of a department shall manage his department.