No, you will not be double-taxed. You will be taxed by NY on the income you earned while in Nebraska as well as the income earned in NY after you moved.
Enter your income earned while in Nebraska as New York nonresident income. The remainder is earned as a New York resident. When you are filling out your Nebraska return, you will not enter any of the income you earned from this job as Nebraska income.
Nebraska's Schedule III instructions state that partial-year residents only enter Nebraska income that is not taxed by another state. Since this income is being taxed by NY due to the convenience of the employer rule, it does not need to be included on your Nebraska return. When asked to allocate your wages from this job, enter 0 as Nebraska sourced in Adjustments to Nebraska Income. That does mean that most, if not all the taxes withheld by Nebraska will be refunded to you and you will owe a large amount to New York.
