Reconfigurable intelligent surfaces (RISs) are envisioned to play a key role in future wireless communication networks. However, channel estimation in RIS-aided wireless networks is challenging due to their passive nature and the large number of reflective elements, leading to high channel estimation overhead. Additionally, conventional methods like beam sweeping, which do not rely on explicit channel state information, often struggle in managing interference in multi-user networks. In this paper, we propose a novel approach that leverages digital twins (DTs) of the physical environments to approximate channels using electromagnetic 3D models and ray tracing, thus relaxing the need for channel estimation and extensive over-the-air computations in RIS-aided wireless networks. To address the digital twins channel approximation errors, we further refine this approach with a DT-specific robust transmission design that reliably meets minimum desired rates. The results show that our method secures these rates over 90% of the time, significantly outperforming beam sweeping, which achieves these rates less than 8% of the time due to its poor management of transmitting power and interference.