Cyber attacks targeting Industrial Control Systems (ICS) have become increasingly sophisticated and hard to identify. Detecting such attacks requires integrating low-level behavioral cues with high-level semantic interpretation, a capability that traditional anomaly detectors lack. This paper presents a Digital Twin (DT)-driven hybrid detection approach that combines deterministic heuristics with systematic, constrained Large Language Model (LLM) reasoning to achieve real-time incident detection. The DT maintains a synchronized, feature-enriched representation of the Secure Water Treatment (SWaT) process, deriving behavioral descriptors. Heuristics identify characteristic signatures of spoofing, valve forcing, denial-of-service, and bias drift, while the LLM is invoked only when heuristics abstain. A constrained JSON schema and semantic plausibility filters ensure physically consistent LLM outputs, and a temporal smoothing layer stabilizes the final decision signal. Evaluation on four canonical SWaT attack scenarios shows that the proposed detector precisely localizes each attack interval with low time-to-detect and zero False Positives (FPs) in the evaluated benign region. Results are consistent across both a local LLaMA model and a cloud-based GPT model, demonstrating the robustness of the constrained hybrid architecture. The findings highlight the potential of DT-guided LLM reasoning as a reliable and interpretable approach to ICS anomaly detection.