I am having some similar problem:
1) I need to find the service area within 5, 10, 15 minutes of the county centroids. When i solve that with the create new service area tool of network analyst it doesn't give the correct answer (it selects the whole state of Texas for some of the points which is wrong. It should create concentric circles around the county centroids with regions at 5, 10, 15 minutes from those points).
2) I am having the same issue with the cities too. When I try to create a service area within 3 hours from San Antonio, Austin, Houston and Dallas it selects the whole of Texas. In fact it should create a circle around the city with areas within 3 hrs from it.
The data is at the following site:
I am attaching a screenshot for this.
i would greatly appreciate if you could kindly look into the matter and get back to me at the earliest.