If, within one year from the payment of any tax or penalty, the payer thereof, or his or her executors, administrators, successors or assigns, makes application for a refund thereof, for the benefit of the person from whom the tax was collected, and the Director of Finance determines that such tax or penalty, or any portion thereof, was erroneously or illegally collected, and that the same can and will be duly refunded to the person from whom the same was collected, the Director of Finance shall pay such amount to the person entitled to such refund, out of the Admission Tax Rotary Fund. For like cause and within the same period, a refund may be so made on the initiative of the Director of Finance, but no refund shall be made of a tax or penalty paid pursuant to a determination of the Director of Finance, as provided for in § 880.12, unless the Director of Finance, after a hearing pursuant to § 880.12, or on his or her own motion, reduced the tax or penalty or it has been established by an appeal to the Common Pleas Court of the County, pursuant to § 880.12, that such determination was erroneous or illegal, in which event a refund shall be made as set forth in this section, upon the termination of such appeal. An application for a refund made as provided in this section shall be deemed a petition for reassessment within the meaning of § 880.12, and the Director of Finance may receive additional evidence with respect thereto. After making his or her determination, the Director of Finance shall give notice thereof to the applicant and the applicant shall have the right to appeal as provided in § 880.12.