Yes, it is true that the nonresident tax return should be completed first.
TurboTax would have completed Georgia first if that was the only one downloaded, even if you disclosed that there was other income from North Carolina.
It would be best to delete Georgia and download North Carolina first. Then, re-add Georgia. During the state interview, start with North Carolina details. But, since your income from North Carolina is exclusive to the rental properties, it could be less essential for you than when people are part-year residents or living in one state and working in another.
For more information, see: How do I file a nonresident state return?
