The brain undergoes profound structural and functional development from childhood to adolescence. Convergent evidence suggests that neurodevelopment proceeds in a hierarchical manner, characterized by heterogeneous maturation patterns across brain regions and networks. However, the maturation of the intrinsic spatiotemporal propagations of brain activity remains largely unexplored. This study aims to bridge this gap by delineating spatiotemporal propagations from childhood to early adulthood. By leveraging a recently developed approach that captures time-lag dynamic propagations, we characterized intrinsic dynamic propagations along three axes: sensory-association (S-A), 'task-positive' to default networks (TP-D), and somatomotor-visual (SM-V) networks, which progress towards adult-like brain dynamics from childhood to early adulthood. Importantly, we demonstrated that as participants mature, there is a prolonged occurrence of the S-A and TP-D propagation states, indicating that they spend more time in these states. Conversely, the prevalence of SM-V propagation states declines during development. Notably, top-down propagations along the S-A axis exhibited an age-dependent increase in occurrence, serving as a superior predictor of cognitive scores compared to bottom-up S-A propagation. These findings were replicated across two independent cohorts (Human Connectome Project: Development and Nathan Kline Institute-Rockland Sample), emphasizing the robustness and generalizability of these findings. Our results provide new insights into the developmental progression of functional dynamics during youth and their role in supporting cognition.