The effectiveness of AI-driven decision-support systems in disaster management depends not only on technical performance but also on whether end users trust and act upon system outputs, a constraint that engineering design alone cannot resolve. A technically superior flood prediction system that citizens choose to ignore during an emergency offers no practical advantage over no system at all. This study examines sociodemographic, cognitive, and dispositional factors that shape public trust in AI-based disaster management systems, with implications for human-centered system design. Using hierarchical ordinal logistic regression applied to survey data from 272 respondents across Peru and Chile (two countries with high exposure to climate-related hazards), we identify a knowledge–trust paradox with direct relevance to deployment strategy: domain knowledge about disasters significantly reduces trust in AI recommendations (β = −0.79), whereas familiarity with AI systems significantly increases it (β = +0.84). Gender (β = +2.11), technological optimism (β = +1.44), and income (β = +0.25) emerge as additional significant predictors. Perceived explainability positively predicts trust, supporting the case for transparent, interpretable outputs as a baseline design requirement rather than an optional feature. These findings suggest that AI systems deployed in life-critical scenarios must account for differences in user knowledge profiles: interfaces designed for domain experts require transparency regarding data integration and uncertainty handling. Broader deployment strategies must also address socioeconomic barriers to access and adoption. The results extend algorithm aversion theory to high-stakes emergency contexts and offer actionable guidance for designing trustworthy, inclusive AI systems for disaster response.