(b) Notwithstanding any other provision of law to the contrary, if the county of Tompkins imposes the additional one-half or one percent rate of tax pursuant to the provisions of section twelve hundred ten of this article, the net collections received by the county of Tompkins on account of such additional rate during the first six months such additional rate is in effect shall be retained by the county of Tompkins to be used for any county purpose. Thereafter, seventy-five per centum of net collections attributable to such additional rate shall be retained by the county of Tompkins, to be used for any county purpose, and the remaining twenty-five per centum of such net collections shall be allocated as follows:

(1) Where the city of Ithaca imposes a tax pursuant to the authority of subdivision (a) of section one thousand two hundred ten of this article, that portion received by the county on account of the additional tax imposed by the county within the city of Ithaca shall be allocated to the city of Ithaca to be used for any city purpose. Where the city of Ithaca does not impose a tax pursuant to the authority of such subdivision (a) of section one thousand two hundred ten the amount required to be allocated to such city, to be used for any city purpose, shall be determined in proportion to such city's population determined as a portion of the county's total population as determined in accordance with the latest decennial federal census or special population census taken pursuant to section twenty of the general municipal law completed and published prior to the end of the quarter for which the allocation is made.

(2) The balance of such twenty-five per centum, after deduction of the amount allocated to the city of Ithaca pursuant to paragraph one of this subdivision, shall be allocated to the towns of such county, and between towns and villages, if any village elects to take its share in cash, in the manner described in subdivision (a) of this section with respect to the area of the county outside the city of Ithaca.