In this context, "on" is the correct choice because it indicates a precise point in time. When we say someone arrived "on time," it means they arrived at the designated time or at the expected time without being late or early. 

- "With" typically indicates accompanying or together, as in "with a friend" or "with a gift."

- "By" usually indicates a deadline or a limit, such as "finish by 5 PM" or "arrive by noon." 
- "In" can indicate a general time frame, such as "in the morning" or "in July."