Check out this link. He clears up a few things that can help get through the run out problem.
An area that's easy to ignore is the shoulder area and the importance in assuring it runs true.
The correct method of measuring depends on exactly what your trying to determine. (and I'm not sure what the NECO tool looks like) but:
The tool you are using is not an incorrect method of determining if the body diameter and neck outside diameter and bullet diameter are coaxial and that is the issue in part.
The tool you are using is probably the most correct of those I have seen on the market. I use a V-Block and indicator ( the indicator I use is not a drop indicator and allows me to access the neck id. I'll post a picture tomorrow.
It is not the method that can tell you if the neck diameters (i.d. and o.d.) are coaxial. (mine is yours isn't)
A drop indicator is really limited to outside measurement of o.d.'s (there are attachments to get to an inside diameter) but the wall or ball micrometer for wall thickness is our tool of choice. If the neck walls are not uniform the diameters are not coaxial. If the walls are not coaxial the bullet will not leave the case in line with the bore.
I have omitted mention of the shoulder diameter BUT if you can adjust your indicator so as to put the stem perpendicular to the shoulder then you could also check the shoulder coaxiality.
If it runs out chances are you will never have good bullet run out or runout tht you are looking for, like .001 or less . Read the link on 6br he talks directly to that relevance.
If the center line through the shoulder (cone) is not in line with the neck i.d the bullet will run out. SEE LINK he has nailed it.