This article presents a Visual Servoing Nonlinear Model Predictive Control (NMPC) scheme for autonomously tracking a moving target using multirotor Unmanned Aerial Vehicles (UAVs). The scheme is developed for surveillance and tracking of contour-based areas with evolving features. NMPC is used to manage input and state constraints, while additional barrier functions are incorporated in order to ensure system safety and optimal performance. The proposed control scheme is designed based on the extraction and implementation of the full dynamic model of the features describing the target and the state variables. Real-time simulations and experiments using a quadrotor UAV equipped with a camera demonstrate the effectiveness of the proposed strategy.