We are not experts in North Carolina law so we would advise you to check with either a NC lawyer, the State Police for North Carolina or the NC Department of Transportation (DOT) to find out under what specific NC state Statute an out of state resident can be cited for driving without insurance in North Carolina.
We can however give you what information we have found on this subject. It appears you referenced in your question North Carolina General Statute 20‑313 which it titled, operation of motor vehicle without financial responsibility a misdemeanor.
Here in section (a) it notes that "On or after July 1, 1963, any owner of a motor vehicle registered or required to be registered in this State who shall operate or permit such motor vehicle to be operated in this State without having in full force and effect the financial responsibility required by this Article shall be guilty of a Class 1 misdemeanor."
This section of NC law does only mention the need for motor vehicles required to be registered or are currently registered in North Carolina to have the type of financial responsibility the state requires them to carry on a vehicle. Auto insurance is the most popular form of financial responsibility for motorist to carry.
A section of the law however that does mention that nonresidents need to have financial responsibility on their vehicle is NCGS 20‑279.5 which is title security required unless evidence of insurance; when security determined; suspension; exceptions.
Subsection (b) of this NC Statute states that the "Commissioner shall, within 60 days after the receipt of a report of a motor vehicle accident, suspend the license of each operator and each owner of a motor vehicle in any manner involved in such accident, and if such operator or owner is a nonresident the privilege of operating a motor vehicle within this State, unless such operator or owner, or both, shall deposit security in the sum so determined by the Commissioner…"
And in subsection C1 it notes that this above section of law shall not apply under to such operator or owner if such owner had in effect at the time of such accident an automobile liability policy with respect to the motor vehicle involved in such accident.
Thus a non-resident of North Carolina can get their license suspended if they are unable to deposit a required security amount to the NC Commissioner of Insurance and have been in an accident without carrying auto insurance (or another accepted type of financial responsibility) on their out of state vehicle.
We contacted someone such at the NC DOT to find out more about if and when an out of state resident in North Carolina can be ticketed for driving without insurance. The DOT representative told us that if you are a NC resident and are driving a vehicle you can get a ticket. You have 30 days to change over your driver’s license and registration if moving to NC from another state. The NC DMV will not come after you regarding driving without insurance if you are a non-resident but law enforcement will the rep noted however she did not know the exact charge.
It may be that you can only be penalized if you are in an accident and without car insurance however the state police or a NC lawyer familiar with this type of law can tell you for certain.
The NC DOT representative suggested contacting the North Carolina Highway Patrol for more information we have done so but without a response back thus far. You can contact them directly yourself if you wish to know under what section of NC law they could ticket you if they found you on the NC roadways driving without insurance as a non-resident.