Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is constructed using continuously differentiable obstacle representations. However, state-of-the-art approaches may suffer from local minima induced by non-convex obstacles, thus failing to scale to complex, high-dimensional joint spaces. On the other hand, sampling-based Model Predictive Control (MPC) techniques provide feasible collision-free paths in joint-space, yet are limited to quasi-reactive scenarios due to computational complexity that grows cubically with space dimensionality and horizon length. To control the robot in the cluttered environment with moving obstacles, and to generate feasible and highly reactive collision-free motion in robots' joint space, we present an approach for modulating joint-space DS using sampling-based MPC. Specifically, a nominal DS representing an unconstrained desired joint space motion to a target is locally deflected with obstacle-tangential velocity components navigating the robot around obstacles and avoiding local minima. Such tangential velocity components are constructed from receding horizon collision-free paths generated asynchronously by the sampling-based MPC. Notably, the MPC is not required to run constantly, but only activated when the local minima is detected. The approach is validated in simulation and real-world experiments on a 7-DoF robot demonstrating the capability of avoiding concave obstacles, while maintaining local attractor stability in both quasi-static and highly dynamic cluttered environments.