Any refund owed as the result of an abatement pursuant to this chapter or any taxpayer action brought pursuant to § 10-27-2, or any other real property tax refund which any governmental entity is required to reimburse for any real property taxes previously received, shall be due and payable to the taxpayer as follows:
(1) If the judicial order or resolution was entered after January first but, before September first, the refund is due on or before the second Monday of January in the year following the entry of judgment or other judicial order requiring the refund or the resolution of abatement.
(2) If the order or resolution was entered between September first through December thirty-first, the refund is due on or before the second Monday of January in the second year following the entry of judgment or other judicial order requiring the refund.