At the time required by law, the county board of supervisors shall levy the taxes necessary for each city fund for the following fiscal year. The levy must be as shown in the adopted city budget and as certified by the clerk, subject to any changes made after a protest hearing, and any additional tax rates approved at a city election. A city levy is not valid until proof of publication or posting of notice of a budget hearing under section 384.16, subsection 3, and the notice and resolution adopted under section 384.15A are filed with the county auditor.