During disasters, individuals witness various dreadful scenes and situations. These scenes and situations generate a sense of panic and cause panic attacks to individuals. Panic attacks cause various disorders like Panic Disorder, Post Traumatic Stress Disorder, and Anxiety Disorder, etc. On the other side, smart cities are becoming the mainstay for urbanization. Hence, the increasing incidents of disruptions due to disasters require the smart cities to adopt emergency response and resilience as the most critical dimension for its design so that the disaster-related risks can be prevented and controlled. This dimension of smart city design helps in minimizing the disruption, human, and socio-economic loss through Information and Communication Technologies (ICT) and called smart disaster management. In this paper, a Fog-Cloud centric Internet of Things (IoT)-based cyber physical framework is proposed, which prioritizes the evacuation of the panicked stranded individuals and provides timely medical support. The physical subsystem of the framework acquires data from stranded individuals and disaster-affected environment and provides various information services to the respective stakeholders (evacuation personnel and stranded individuals). Whereas, the cyber subsystem of the proposed framework, initially at the Fog layer classifies the Panic Health Status (PHS) of the stranded individuals in real-time based on the acquired health data and analyzes the novelty of the data for avoiding unnecessary data traffic to Cloud. After PHS diagnosis, the cyber subsystem uses Bayesian Belief Network (BBN) to monitor the panic health sensitivity of the stranded panicked individuals using disaster-related health and environmental data, at the Cloud layer. This subsystem also builds the evacuation map using acquired disaster-related environmental data at the Cloud layer. Based on the evacuation map and monitored panic health sensitivity of the individuals, the subsystem prepares evacuation strategy, which prioritizes the evacuation of the stranded individuals. The vital points of this proposed framework are the immediate panic-related diagnostic and curative alert generation to the mobile devices of the stranded individuals from the Fog layer, and the preparation of the evacuation strategy based on the evacuation map and panic health sensitivity monitoring of the stranded individuals, at the Cloud layer. The experimental evaluation of the proposed framework depicts the classification efficiency of Support Vector Machine (SVM) for classifying the PHS of the stranded individuals in real-time, and efficiency of Data Novelty Analysis (DNA) for avoiding unnecessary data traffic, at the Fog layer. The experimental evaluation also acknowledges the efficiency of evacuation map building using Unmanned Aerial Vehicles (UAVs), and panic health sensitivity monitoring using BBN at the Cloud layer.