Robot-assisted surgical systems have demonstrated significant potential in enhancing surgical precision and minimizing human errors. However, existing systems cannot accommodate individual surgeons' unique preferences and requirements. Additionally, they primarily focus on general surgeries (e.g., laparoscopy) and are unsuitable for highly precise microsurgeries, such as ophthalmic procedures. Thus, we propose an image-guided approach for surgeon-centered autonomous agents that can adapt to the individual surgeon's skill level and preferred surgical techniques during ophthalmic cataract surgery. Our approach trains reinforcement and imitation learning agents simultaneously using curriculum learning approaches guided by image data to perform all tasks of the incision phase of cataract surgery. By integrating the surgeon's actions and preferences into the training process, our approach enables the robot to implicitly learn and adapt to the individual surgeon's unique techniques through surgeon-in-the-loop demonstrations. This results in a more intuitive and personalized surgical experience for the surgeon while ensuring consistent performance for the autonomous robotic apprentice. We define and evaluate the effectiveness of our approach in a simulated environment using our proposed metrics and highlight the trade-off between a generic agent and a surgeon-centered adapted agent. Finally, our approach has the potential to extend to other ophthalmic and microsurgical procedures, opening the door to a new generation of surgeon-in-the-loop autonomous surgical robots. We provide an open-source simulation framework for future development and reproducibility at https://github.com/amrgomaaelhady/CataractAdaptSurgRobot.