This paper presents a new flight control framework for tilt-rotor multirotor uncrewed aerial vehicles (MRUAVs). Tiltrotor designs offer full actuation but introduce complexity in control allocation due to actuator redundancy. We propose a new approach where the allocator is tightly coupled with the controller, ensuring that the control signals generated by the controller are feasible within the vehicle actuation space. We leverage nonlinear model predictive control (NMPC) to implement the above framework, providing feasible control signals and optimizing performance. This unified control structure simultaneously manages both position and attitude, which eliminates the need for cascaded position and attitude control loops. Extensive numerical experiments demonstrate that our approach significantly outperforms conventional techniques that are based on linear quadratic regulator (LQR) and sliding mode control (SMC), especially in high-acceleration trajectories and disturbance rejection scenarios, making the proposed approach a viable option for enhanced control precision and robustness, particularly in challenging missions.