If the contest proceeds in more than one county, and the nominee is to be certified by the Secretary of State from the compilation of election returns in his or her office, the judgment in each county in which there has been a contest shall show what, if any, changes in the returns in the office of the Secretary of State relating to that county ought to be made. Certified copies of the judgments shall be served upon the Secretary of State. He or she shall make the changes in the record in his or her office as each judgment requires, and conform his or her compilation and his or her certificate of nomination accordingly.