Elvish Refueler's ability is (I think) bugged
During the first match of a limited match, I activated Elvish refueler's Exhaust ability during my opponent's turn. Then, during my turn, I activated it again (because it was the first activation during my turn, and her ability says you can use exhaust abilities as though they haven't been activated if you haven't exhausted yet during your turn). It worked fine. Then my opponent cast a vehicle that exiled my elvish refueler until it left the battlefield. I exiled that vehicle, so my elvish refueler came back. I was able to use her exhaust ability again on my opponent's turn, but when it was my turn again, I could not use her or any other creature's exhaust ability, despite not having activated.

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odango#82975 commented
I also checked.
There is definitely a bug.
It seems that your opponent can use the usage rights without your permission.Sorry for the Japanese, but I am attaching a video post that reproduces it.
https://x.com/goodbey2nd/status/1889653146504343568