If you are working out of state for your employer's convenience (they want you to work from home, they don't provide an office), then you only owe NY tax for the days you actually live or work in New York State. (2 weeks per year is 3.85%, not 1%). You will prepare a non-resident return for NY and you will need to manually allocate your income (how much was earned while living or working in NY, even temporarily). Then, file a resident return for your home state reporting all your world-wide income, and your home state will give you a tax credit agains the tax you paid in NY.
If you are working out of state for your own convenience, you must pay NY income tax on all your NY income. You would still file a NY non-resident return, and you would manually allocate your income, but in this case it would be all your wages from that job. Note that other income, like investments, prizes, bank interest and so on, is only taxed where you live. Again, you file a resident return for your home state reporting all your world-wide income, and your home state will give you a tax credit agains the tax you paid in NY.
Here is the NY tax memo setting out the factors used to determine the convenience of the employer rule.
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
