When you made your route, did you select a region? If you didn't, the default region doesn't have cars. To check or change the route setting select the route, then select Edit Route and in the click Main Menu and select Edit Route.
I knew about the "don't select default region" rule to get cars, but then what do the car spawn splines accomplish? I have used them to get cars to go on roads they would not otherwise gone on, but I certainly have no good understanding as to how to use them effectively.