Does employer have to issue corrected W2 if I put wrong state on W4? If not, how do I enter the right amounts in my state returns?

Hi. I need to amend my 2018 state returns, because I realized after I filed that my withholding should've been for a different state. (My fault - I had submitted a state W4 for the wrong state. I live & work in NY, while my employer is in MA, and my W4 was for MA. Oops!) Payroll tells me they don't issue corrected W2's in that situation.

1. Should I push back on Payroll? Are they required to issue a corrected W2 now?

2. If I don't get a corrected W2, when I amend my state returns, how do I indicate that my state wages are different from what shows on the W2? (It should be $0 in MA and the full amount in NY.)

Thanks!