Your W-2 is not correct. As you surmised, the box 16 amount, for the line with NY in box 15, should only be $10,000. If you cannot get a corrected W-2 from your employer, the workaround, in TurboTax (TT), is to change the box 16 amount at the W-2 screen. That should get TT to do the right calculation. There's still the risk that the NY Department of Taxation and Finance may not accept that calculation, since your W-2 says otherwise.
Even the $10,000 may not have been subject to NY tax, depending on the details. See TomD8's reply.
