In complex operational environments, signal ambiguity and false alarms make task allocation for multiple unmanned aerial vehicles (UAVs) challenging. To address this problem, we propose the Bayesian Rolling Information-Theoretic Reconnaissance Action Assignment (RITRA) framework. RITRA integrates Bayesian belief tracking, expected information gain (EIG), and a cooperative criticality model based on Shapley values in a unified receding-horizon strategy. By assessing reconnaissance and intervention utilities for each UAV–hazard pair, RITRA casts mission planning as a dynamic optimization problem. We use an enhanced Hungarian algorithm with idle states, allowing UAVs to remain on standby when no deployment has positive expected value. Ablation results indicate that combining Bayesian tracking, active information collection, and risk-aware execution contributes to robust performance under the evaluated uncertainty conditions. In the 200-run paired Monte Carlo stress test, RITRA achieved a mean mission utility of 9.4362, a normalized mission score of 0.7890, and 0.245 false deployments per run. Against the best-performing baseline, a CBBA-based allocation method, RITRA achieved a mean paired mission-utility gain of 1.4925. On publicly released dynamic MRTA instances augmented with false-alarm uncertainty, RITRA achieved the highest aggregate mission utility, normalized mission score, and mission accuracy among the compared controllers, providing additional evidence of its effectiveness. These results indicate that RITRA supports risk-aware multi-UAV allocation under the evaluated uncertain conditions.