If one earns income from home as a consultant to an organization in another state, does that count as making money in another state?

If you were paid by the organization and the organization withheld state taxes for the other state, then you will want to file a return to get the taxes paid to that state refunded to you.  You will   If there was no withholding then you don't need to file, but the money will be added to your return for you state of residence if your state has a state income tax.

Thanks, I understand the concept, but TurboTax is simply asking yes or no.  The work generated a Form 1099-NEC.  Does this count as making money in another state if the work was done without physically visiting that state.

That does not count unless there are amounts in Boxes 5 and 7 on the 1099-NEC