The demand for more safe and durable roads, combined with the need to preserve the environment, led to the production and application of asphalt–rubber (AR) on roads. Nevertheless, this complex material needs further study in order to better distinguish among the phenomena that take place during AR production, as they impact on the final product characteristics. Here, we effectively quantify the rheological changes related to bitumen aging due to diffusion of small molecules of bitumen into the rubber particles and to the release of fillers from rubber into the bitumen during AR production. “A sphere AR production simulator” was developed to assess AR aging independently. The comparison of the characteristic relaxation times of both AR and simulated AR shows that the aging alone cannot explain the rheological changes during AR production. The extent of the changes related to the combined effects of aging and filler release increases as the bitumen used to produce AR is softer.