What's interesting is that Clover seems to have already been aware of Yotsuha's rewinding of time or at least aware of its possibility and connected the idea when they found out about the watch.
If they knew nothing, just hearing about the watch wouldn't be enough to figure out what it does. On the contrary, they seemed not only suspicious of Yotsuha's "perfect runs", but ready to accept a supernatural answer and connect it to time travel specifically. Even the wording seems to imply that they already knew she had the power and just didn't know the source of it.
It seems likely that Clover has either experienced time travel themselves (or knows someone who has) or they are aware of the timeline changes by Yotsuha in some way. I hesitate to say that they are also able to time travel currently (at least not in a similar way to Yotsuha) or she would else meet a lot more resistance to her plans and a lot more unpredictable changes to the timeline in response to her own. Them being somehow aware of the time travel or at least having some other power that would easily tick them off as to what she's doing probably makes more sense (at least if Clover isn't the brother who already knows about the time travel, but that doesn't feel like the answer).
Considering how DIY the origin of Yotsuha's power is it's not unreasonable that someone like Clover equally determined and emotionally charged as Yotsuha was when she wanted to save Uichi would also develop a power to help them achieve that. Also, considering that Yotsuha received a power that was more or less exactly what she need to achieve her goal, it's likely that Clover also received a power fitting to their goal. Some kind of clairvoyance that allows them to know who to use to take down Uichi and potentially also to be able to realise that the timeline has changed could be possible. Even then I guess it might be somewhat time-themed, i.e. seeing the future, past or alternative timelines.
Alternatively, they have the same or a similar power, but their time device already broke like Yotsuha's is going to. In a way, this may be the most thematically fitting option that also makes sense of the data we currently have.