In high-stakes disaster scenarios, timely, context-aware decisions are essential for survival. Traditional AI systems deliver speed and scale but often lack the intuitive reasoning and adaptive cognition exhibited by human experts. This study presents TruCrisisAware, a mobile AI framework grounded in Dual-Process Theory (DPT) and the Recognition-Primed Decision (RPD) model. By combining heuristic (System 1) and deliberative (System 2) reasoning, and dynamically switching between them based on situational demands and inferred user trust, the system emulates expert decision-making under uncertainty. Implemented as a smartphone app, TruCrisisAware fuses sensor data (e.g., smoke, heat, visual obstruction) with triangulated positioning to provide real-time evacuation guidance. The decision engine is trained via imitation and reinforcement learning. Six simulated fire scenarios in Unity ML-Agents evaluate the system on Task Success Rate (TSR), Route Optimality (RO), Decision Robustness (DR), and Trust Calibration Index (TCI). Results show that TruCrisisAware outperforms single-mode agents, maintaining high performance and trust alignment under complex conditions. The system offers a human-centered decision support model that bridges speed and cognition to enhance safety, coordination, and resilience in disaster contexts.