Disaster logistics is inherently governed by temporal urgency and spatial risk heterogeneity, often under conditions of deep uncertainty. While traditional stochastic programming models address demand uncertainty, they typically overlook the dynamic risk evolution and time-critical allocation shifts essential to disaster response. This paper introduces a time-indexed stochastic optimization framework for disaster logistics that incorporates risk profile-based resource allocation. The model defines high-, medium-, and low-risk zones using evolving scenario inputs and ties their urgency to indexed decision stages. Leveraging multi-period MILP formulations from existing OR literature [4, 5, 9], the model integrates Conditional Value-at-Risk (CVaR) [7] and risk-weighted priority functions to dynamically guide allocation over time. Scenario-based risk evolution and real-time adjustments are further supported through techniques inspired by recent metaheuristic and hurricane logistics work [11, 12]. Computational experiments demonstrate that the proposed model significantly outperforms static or uniform-priority stochastic frameworks in minimizing both expected shortages and tail-risk-driven failures. This research contributes a novel decision-support paradigm that aligns stochastic optimization with temporal urgency and risk stratification, offering critical insights for real-time, resilient disaster operations.