The board may employ necessary assistants, officers, experts, and such other employees as it deems necessary. All such personnel of the board shall be under the supervision of the chairman of the board or an executive officer to whom he delegates such responsibility. All such personnel shall be appointed pursuant to the State Civil Service Act (Part 1 (commencing with Section 18000) of Division 5 of Title 2 of the Government Code), except for the one exempt deputy or employee allowed by subdivision (e) of Section 4 of Article XXIV of the California Constitution.