This paper studies the kinematic tracking control problem for aerial manipulators. Existing kinematic tracking control methods, which typically employ proportional-derivative feedback or tracking-error-based feedback strategies, may fail to achieve tracking objectives within specified time constraints. To address this limitation, we propose a novel control framework comprising two key components: end-effector tracking control based on a user-defined preset trajectory and quadratic programming-based reference allocation. Compared with state-of-the-art approaches, the proposed method has several attractive features. First, it ensures that the end-effector reaches the desired position within a preset time while keeping the tracking error within a performance envelope that reflects task requirements. Second, quadratic programming is employed to allocate the references of the quadcopter base and the Delta arm, while considering the physical constraints of the aerial manipulator, thus preventing solutions that may violate physical limitations. The proposed approach is validated through three experiments. Experimental results demonstrate the effectiveness of the proposed algorithm and its capability to guarantee that the target position is reached within the preset time.