Following establishment of a sewer district with an appointed board, the chief executive officer of the city shall appoint two members and the county commission shall appoint three members to the sewer district board of directors. The board members shall serve without compensation for terms of four years and until their successors are appointed and qualified; provided, however, that of the initial appointments by the mayor one shall be for a term of one year and one shall be for a term of two years and of the initial appointments by the county commission, one shall be for one year, one for two years and one for three years. A vacancy shall be filled by the mayor or the county commission depending on who made the initial appointment.