Banks receive millions of reports of fraud, scams, and disputed transactions every year, making it challenging to accurately direct customers to the appropriate specialist teams for assistance. The existing manual process driven by humans is slow and stressful for both customers and staff. To address this, we develop a customer-facing AI powered triaging agent that leverages large language models (LLMs) to conduct multi-turn conversations, ask relevant questions, and classify cases for accurate, policy-guided routing, making it embedded in the customer journey. To evaluate and continuously improve the agent, synthetic digital twins of real customers were simulated, generating realistic, labelled dialogues based on historical data to test a wide range of real-world scenarios. This work details the triage agent's modelling approach, integration with policy, safety guardrails and reasoning frameworks, the use of the synthetic agent for scalable evaluation, and findings on the AI system's accuracy, robustness, and compliance. Results show that the agent successfully improves triaging of historical cases, achieving a 30.6% increase in classification accuracy, with high satisfaction levels reported by our subject-matter experts, highlighting how targeted probing can lead to more effective triage in banking operations at scale.