Reactive motion generation in dynamic and unstructured scenarios is typically subject to essentially static perception and system dynamics. Reliably modeling dynamic obstacles and optimizing collision-free trajectories under perceptive and control uncertainty are challenging. This article focuses on revealing tight connection between reactive planning and dynamic mapping for manipulators from a model-based perspective. To enable efficient particle-based perception with expressively dynamic property, we present a tensorized particle weight update scheme that explicitly maintains obstacle velocities and covariance meanwhile. Building upon this dynamic representation, we propose an obstacle-aware MPPI-based planning formulation that jointly propagates robot-obstacle dynamics, allowing future system motion to be predicted and evaluated under uncertainty. The model predictive method is shown to significantly improve safety and reactivity with dynamic surroundings. By applying our complete framework in simulated and noisy real-world environments, we demonstrate that explicit modeling of robot-obstacle dynamics consistently enhances performance over state-of-the-art MPPI-based perception-planning baselines avoiding multiple static and dynamic obstacles.