I called New York State Department of Finance and they said that I'm being refunded the full amount of the dispute, $18.52. While on the phone with them, they did the computation by hand and said that the numbers on my return, as done by TurboTax, are correct. Since I'm getting a full refund, it's clearly their error. I asked them the reason for the discrepancy, and they said that I'll be getting a notice in the mail describing the reason.
I'll share it with you when it arrives.