LLMs have shown strong performance on human-centric reasoning tasks. While previous evaluations have explored whether LLMs can infer intentions or detect deception, they often overlook the individualized reasoning styles that influence how people interpret and act in social contexts. Social deduction games (SDGs) provide a natural testbed for evaluating individualized reasoning styles, where different players may adopt diverse but contextually valid reasoning strategies under identical conditions. To address this, we introduce InMind, a cognitively grounded evaluation framework designed to assess whether LLMs can capture and apply personalized reasoning styles in SDGs. InMind enhances structured gameplay data with round-level strategy traces and post-game reflections, collected under both Observer and Participant modes. It supports four cognitively motivated tasks that jointly evaluate both static alignment and dynamic adaptation. As a case study, we apply InMind to the game Avalon, evaluating 11 state-of-the-art LLMs. General-purpose LLMs, even GPT-4o frequently rely on lexical cues, struggling to anchor reflections in temporal gameplay or adapt to evolving strategies. In contrast, reasoning-enhanced LLMs like DeepSeek-R1 exhibit early signs of style-sensitive reasoning. These findings reveal key limitations in current LLMs' capacity for individualized, adaptive reasoning, and position InMind as a step toward cognitively aligned human-AI interaction.