When your work duties commence it appears you will be working in New York, so that may take precedent over your current job situation. It would be different if you were currently working remotely. But since the income is an advance on work you will be doing as a New York resident, it is likely New York income.
The normal primary considerations are if you have an office in New York that you work out of at least occasionally and does your employer require you to work from home? If the answer to both of these questions is "no" then you would have a case for your income not being taxable in New York. But that would likely only apply if you were actually working.
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