My son is an Ohio resident working in New York City this semester. His employer is withholding Ohio state taxes, but not NY taxes from his checks. Is this correct?

 He worked in NYC last year for another employer, and they withhold NY not Ohio (and he filed nonresident NY return and Ohio resident return where he got credit for NY taxes). It seems the employer this year isn't doing it correctly? Shouldn't the be withholding for NY taxes (not Ohio)?