Anomaly detection is increasingly becoming crucial for maintaining the safety, reliability, and efficiency of industrial systems. Recently, with the advent of digital twins and data-driven decision-making, several statistical and machine-learning methods have been proposed. However, these methods face several challenges, such as dependence on only real sensor datasets, limited labeled data, high false alarm rates, and privacy concerns. To address these problems, we propose a suite of digital twin-integrated federated learning (DTFL) methods that enhance global model performance while preserving data privacy and communication efficiency. Specifically, we present five novel approaches: Digital Twin-Based Meta-Learning (DTML), Federated Parameter Fusion (FPF), Layer-wise Parameter Exchange (LPE), Cyclic Weight Adaptation (CWA), and Digital Twin Knowledge Distillation (DTKD). Each method introduces a unique mechanism to combine synthetic and real-world knowledge, balancing generalization with communication overhead. We conduct an extensive experiment using a publicly available cyber-physical anomaly detection dataset. For a target accuracy of 80%, CWA reaches the target in 33 rounds, FPF in 41 rounds, LPE in 48 rounds, and DTML in 87 rounds, whereas the standard FedAvg baseline and DTKD do not reach the target within 100 rounds. These results highlight substantial communication-efficiency gains (up to 62% fewer rounds than DTML and 31% fewer than LPE) and demonstrate that integrating DT knowledge into FL accelerates convergence to operationally meaningful accuracy thresholds for IIoT anomaly detection.