Here's how it works:
New York can tax non-residents on income earned from work physically performed or carried out within New York State. So YES, you do owe New York State income tax on that portion of your earnings.
New York is no different in this respect than any other state with an income tax.
If your resident state has an income tax, your NY earnings would also be taxable there, because your resident state can tax ALL your income, regardless of where you earn it.
You'll be able to claim a credit on your home state return for the tax you pay to NY on the dollars taxed by both, so you won't be double-taxed. But you must file a tax return in both states.
This TurboTax help article explains how to file a non-resident state tax return:
How do I file a nonresident state return? (intuit.com)
So your employer was correct in providing you with a New York W-2 for 2018. And since you did physically work in NY that year, you would in fact owe NY taxes.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
