No, it is not necessary to back roll the finish paint after priming it, assuming you back rolled the primer. This depends on what you are painting; the roughness, excessive porosity, etc.

Once the surface has been properly primed and allowed to dry according to the manufacturer’s instructions, applying the finish coat directly on top of the primer is sufficient for achieving a smooth and consistent finish.

Back rolling, which involves rolling over the painted surface with a “dry roller” to even out the application, is typically done to help spread the paint more evenly and remove roller marks or push paint into the surface. However, this step is usually reserved for textured surfaces or when using certain types of paint that may benefit from back rolling to achieve a desired finish. For most standard applications, applying the finish coat directly after priming and ensuring proper technique during painting should result in a satisfactory end result without the need for back rolling.