Human migration is one of the defining topics of our time, but the dynamics of when and how often migration events occur are poorly understood. Often, a single, context-unaware model is assumed without empirical evidence. Spatiotemporal dependencies and heterogeneities cannot be explained by such a viewpoint. These gaps produce misunderstanding of migration, leading to imprecise predictions and ineffective responses. To address the gaps, we make use of recent advances in data collection and quantitative techniques, investigating Somali internal migration as a case study. We find that whether migration timings are independent (Poisson) or interdependent (bursty) depends on their coincidence with conflicts and extreme weather events. Interdependent migration timings are often observed in peaceful districts, while independent dynamics are found in those with higher coincidence of migration and conflict-involved stressors. These findings help us identify whether migration is self-induced or externally driven, develop more predictive models, and build context-specific migration policies.