Jimmy reflected on his fight with Harry and noticed an issue: his mental reaction speed was sufficient for him to locate and follow Harry's movements, but the action of firing his gun was slightly delayed, resulting in his shots being just a hair off target. This was still a discrepancy between body and mind, indicating the need for continued training to improve his shooting skills and speed to better sync with his mental processes.
For the average person, Jimmy had no problem, but against top-notch experts, their sixth sense was very sharp. Harry dodged Jimmy's intentional shot the moment he entered the door, which was definitely not because he saw Jimmy firing, but due to his danger perception ability prompting him to move subconsciously to evade.