Noninvasive brain-computer interfaces (BCIs) allow to interact with the external environment by naturally bypassing the musculoskeletal system. Making BCIs efficient and accurate is paramount to improve the reliability of real-life and clinical applications, from open-loop device control to closed-loop neurorehabilitation. By promoting sense of agency and embodiment, realistic setups including multimodal channels of communication, such as eye-gaze, and robotic prostheses aim to improve BCI performance. However, how the mental imagery command should be integrated in those hybrid systems so as to ensure the best interaction is still poorly understood. To address this question, we performed a hybrid EEG-based BCI training involving healthy volunteers enrolled in a reach-and-grasp action operated by a robotic arm. Main results showed that the hand grasping motor imagery timing significantly affects the BCI accuracy evolution as well as the spatiotemporal brain dynamics. Larger accuracy improvement was obtained when motor imagery is performed just after the robot reaching, as compared to before or during the movement. The proximity with the subsequent robot grasping favored intentional binding, led to stronger motor-related brain activity, and primed the ability of sensorimotor areas to integrate information from regions implicated in higher-order cognitive functions. Taken together, these findings provided fresh evidence about the effects of intentional binding on human behavior and cortical network dynamics that can be exploited to design a new generation of efficient brain-machine interfaces.