We present a control methodology for underactuated aerial manipulators that is both easy to implement on real systems and able to achieve highly dynamic behaviours. The method is composed by two parts, a nominal input/state generator that takes into account the full-body nonlinear and coupled dynamics of the system, and a decentralized feedback controller acting on the actuated degrees of freedom that confers the needed robustness to the closed-loop system. We show how to apply the method to Protocentric Aerial Manipulators (PAM) by first using their differential flatness property on the vertical 2D plane in order to generate dynamical input/state trajectories, then statically extending the 2D structure to the 3D, and finally closing the loop with a decentralized controller having the dual task of both ensuring the preservation of the proper static 3D immersion and tracking the dynamic trajectory on the vertical plane. We demonstrate that the proposed controller is able to precisely track dynamic trajectories when implemented on a standard hardware composed by a quadrotor and a robotic arm with servo-controlled joints (even if no torque control is available). Comparative experiments clearly show the benefit of using the nominal input/state generator, and also the fact that the use of just static gravity compensation might surprisingly perform worse, in dynamic maneuvers, than the case of no compensation at all. We complement the experiments with additional realistic simulations testing the applicability of the proposed method to slightly non-protocentric aerial manipulators.