I think there is a small bug. Please look at the picture below. Since bounty period ended 23 hours ago, its grace period should not be ended yet. But it says it did.
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In my opinion, this is a bug, and it has nothing to do with when the hourly job runs.
As you can see, the bounty was added at 16:25, but the grace period expired at 15:25.
I haven't been awarded the bounty yet and I don't know when it will happen, but the grace period either hasn't ended yet or it was only 23 hours long.