The Vehicular Digital Twin Network (VDTN) integrates digital twin (DT) models of connected and autonomous vehicles (CAVs) to facilitate smart sensing, management, and collaboration in the physical realm. VDTN synchronizes extensive data on roads, vehicles, and operators, including sensitive information like user location and driving habits. To address these privacy concerns and enhance model efficiency, we introduce a time-sensitive local differential privacy-based federated learning framework (FedTS) tailored for VDTN. This framework assigns varying privacy levels to DT models during model-sharing intervals, considering the time-sensitivity of VDTNs. Comparative analysis with state-of-the-art algorithms, such as differentially-private stochastic gradient descent (DP-SGD), demonstrates significant improvements in both security and model performance.