The decentralized digital media landscape has diversified agenda-setting actors, creating challenges like misinformation and emotional amplification that complicate crisis communication. This study investigates the temporal dynamics of traditional media, social media, and public agendas during crisis events, using the Cathay Pacific incident as a representative case of transnational media discourse. Drawing on agenda-setting theory and the public opinion lifecycle model, it applies ARIMA time-series modeling, social network analysis, and Granger causality testing to analyze interactions and lag structures among communication actors across different stages of crisis evolution. Empirically, the study identifies a distinct 40-hour lag between the peak agenda-setting effectiveness of social and traditional media during the early phase of public opinion formation. Social media demonstrated the highest temporal responsiveness within the first 24 hours, with its influence declining after the sixth day, whereas traditional media exhibited delayed but sustained impact on the agenda. These findings reveal that agenda-setting operates through recursive, time-sensitive influence cycles rather than linear dissemination. By integrating theoretical refinement and practical relevance, this study advances temporal agenda-setting research by quantifying cross-platform lag interactions and modeling bidirectional media–public dynamics. The findings further inform crisis communication management, underscoring the need for synchronized cross-platform timing and proactive interventions to preempt misinformation and foster rational public discourse.