The tax collector shall record the diagram and assessment received pursuant to Section 10401 in a substantial book to be kept for that purpose in his office. Upon the date of recordation with the tax collector or, if a certified copy is recorded with the county surveyor or the superintendent of streets of the city, or both, as provided in Section 10401, then upon the date of recordation, the assessment becomes due and payable, except that the legislative body may provide in the resolution adopted pursuant to Section 10312 that all or any portion of the assessment becomes due and payable on the date of the bonds which represent the assessments or portion thereof.