No, it is not necessary. The reason why is that the income you earned in New York is taxed in New York as a nonresident. The fact that you were paid by a company in Illinois does not change this.
The nonresident business allocation is filled out when some of the wages stated as being earned in New York as a nonresident were actually earned in another state. However, if all that is reported to New York was earned in New York, no allocation (dividing, splitting) is needed.
The income is not allocated in the state where you live (sounds like Illinois), because your resident state taxes all of your income. You will claim a credit on your resident state return for the tax you pay to NY on the income you earn in New York, but your resident state taxes all of your income otherwise.
You do want to prepare the nonresident return first for TurboTax to calculate the credit correctly.
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