County employees assigned to the office of the county superintendent of schools shall cease to be employees of the county upon the establishment of a separate budget for the office of the county superintendent of schools, and shall thereafter be paid from the county school service fund. Other county employees assigned to functions transferred to the county board of education pursuant to Article 3 (commencing with Section 1080) of Chapter 1 of this part shall cease to be employees of the county upon the effective date of such transfer, and shall thereafter be paid from the county school service fund.