Despite extensive developments in motion planning of autonomous aerial vehicles (AAVs), existing frameworks faces the challenges of local minima and deadlock in complex dynamic environments, leading to increased collision risks. To address these challenges, we present TRUST-Planner, a topology-guided hierarchical planning framework for robust spatial-temporal obstacle avoidance. In the frontend, a dynamic enhanced visible probabilistic roadmap (DEV-PRM) is proposed to rapidly explore topological paths for global guidance. The backend utilizes a uniform terminal-free minimum control polynomial (UTF-MINCO) and dynamic distance field (DDF) to enable efficient predictive obstacle avoidance and fast parallel computation. Furthermore, an incremental multi-branch trajectory management framework is introduced to enable spatio-temporal topological decision-making, while efficiently leveraging historical information to reduce replanning time. Simulation results show that TRUST-Planner outperforms baseline competitors, achieving a 96\% success rate and millisecond-level computation efficiency in tested complex environments. Real-world experiments further validate the feasibility and practicality of the proposed method.