A district which is converted under the provisions of this subchapter shall be constituted a district operating under Article XVI, § 59, of the Texas Constitution and shall be governed by the provisions of Chapter 62 of this code as if it had originally been organized under Article XVI, § 59, of the Texas Constitution, except the commissioners of a converted district shall be appointed in the manner that initial commissioners are appointed under Sections 62.061 and 62.062 of this code.