Notwithstanding the provisions of sections fifteen hundred sixteen, fifteen hundred seventeen and fifteen hundred eighteen or any other provisions of law to the contrary:
(a) If the city council has not fixed the tax rates for the ensuing fiscal year pursuant to section fifteen hundred sixteen on or before the fifth day of June, the commissioner of finance shall be authorized to complete the assessment rolls using estimated rates and to collect the sums therein mentioned according to law. The estimated rates shall equal the tax rates for the current fiscal year.
(b) If, subsequent to the fifth day of June, the council shall, pursuant to section fifteen hundred sixteen, fix the tax rates for the ensuing fiscal year at percentages differing from the estimated rates, real estate tax payment shall nevertheless be payable in accordance with subdivision a of this section at the estimated rates. However, in such event, prior to the first day of January in such fiscal year, the commissioner of finance shall cause the completed assessment rolls to be revised to reflect the tax rates fixed by the council pursuant to section fifteen hundred sixteen, and an amended bill for the installment or installments for such fiscal year due and payable on or after the first day of January shall be submitted to each taxpayer in which whatever adjustment may be required as a result of the estimated bill previously submitted to the taxpayer shall be reflected.