Agentic AI is emerging, capable of executing tasks through natural language, such as Copilot for coding or Amazon Rufus for shopping. Evaluating these systems is challenging, as their rapid evolution outpaces traditional human evaluation. Researchers have proposed LLM Agents to simulate participants as digital twins, but it remains unclear to what extent a digital twin can represent a specific customer in multi-turn interaction with an agentic AI system. In this paper, we recruited 40 human participants to shop with Amazon Rufus, collected their personas, interaction traces, and UX feedback, and then created digital twins to repeat the task. Pairwise comparison of human and digital-twin traces shows that while agents often explored more diverse choices, their action patterns aligned with humans and yielded similar design feedback. This study is the first to quantify how closely LLM agents can mirror human multi-turn interaction with an agentic AI system, highlighting their potential for scalable evaluation.