In JoJo's Bizarre Adventure, Jotaro seems able to move even while Dio stops the time. On the other hand, Dio can't when Jotaro stops the time.
Why?
Source: DIO's World, Part 3 (DIOの世界 その3, DIO no Sekai Sono San) the forty-seventh episode of Stardust Crusaders
Jotaro planned to stop time when the limit of DIO's time stop was finishing.
This happened when Jotaro did the finishing blow after he survived the road roller attack.
And when DIO stopped time, Jotaro can't use the ability but can feel the situation in this case of "time stop world", but when he can move, Jotaro can trigger the ability while he is in DIO's stopped time by use his time limit between DIO's stopped time and the end of it triggering.
He basically counters DIO's stopped time.
I think Dio can't move in Jotaro's stopped time after the Road Roller attack because he already used up his stopped time.
I assume Dio would actually be able to move in Jotaro's stopped time if he didn't already use up all his stopped time during the Road Roller attack before, but since that's the only time Jotaro uses his stopped time during the battle against Dio we can just assume that he would be able to move in that case.
Actually, you don't need to think so hard to understand it. Just consider Jotaro fighting Dio at the start, where Dio throwed knives at Jotaro. Jotaro uses his time_limit(Capacity in seconds to stop time) and can't move after it, until time resumes again. This same applies to Dio, he can't stop time again until time resumes.
DIO actually can move in Jotaro's time stop. While DIO was counting after nine thinking his time stop ability was improving, he was actually using his time to be able to move in Jotaro's timestop which is three seconds. That's why he stopped at 11 seconds before he couldn't move.
