The members of the county school board shall be appointed or reappointed, as the case may be, for terms of four years each, except that initial appointments hereunder may be for terms of one to four years, respectively, so as to provide staggered terms for such members. Notwithstanding the foregoing provisions of this section, the terms of office of the school board members in a county which is contiguous to a county having the urban county executive form of government shall begin on July 1 of the year in which the board of supervisors takes office following the next general election for supervisors. However, all other applicable provisions of Titles 22.1 and 15.2 pertaining to the powers and duties of school boards and their appointments shall continue to apply to the members of such school board.