With the development of intelligent transportation systems (ITS), digital twin (DT) technology is becoming increasingly widespread in the application of connected automated vehicles (CAV) to enhance driving safety. However, when DT systems are used for driving safety decisions through virtual control of reality and virtual reflection of reality, decision errors may occur, which can be fatal for the driving safety of CAVs. The main reasons are attributed to three aspects: the accuracy, the communication delay, and the safety control of the DT system. In this paper, we study to improve the accuracy and safety of the DT system decisions with communication delay. Firstly, we considered powertrain factors to construct a high-precision and high-fidelity DT system. We use the goodness-of-fit functions (GoFs) and measure-of-performances (MoPs) to fit the vehicle's model and carry out error measurements in the DT system. Secondly, we analyze the stability of the DT system using plant stability and string stability under time delay. The effective range of time delay ensures the accuracy and stability of the DT system, and provides a safety constraint for the design of the CAV's controller. Finally, we propose a DT-assisted robust safety-critical traffic control (RSTC) strategy based on control barrier functions (CBFs). This strategy ensures the driving safety of CAVs with preceding and following vehicles while maintaining traffic stability. The theoretical analysis and experimental results present that the proposed scheme can effectively avoid conflicts and crash risks to ensure driving safety.