Ah yes, what to do on those days in the year when there are 23 or 25 hours in a day, and when hours can either be skipped completely or recur twice.
And should a once-daily job be handled differently than an hourly job? Presumably you want an hourly job to recur twice (once for each occurence of the same hour), whereas you want the once-daily job to occur only once that day - so there isn't necessarily one rule that fits all.
Personally, I would suggest that the best approach is simply not to schedule things in the 0100-0159 period, when possible. Once a year on a certain date, times in this range simply do not occur, and once a year on a certain (different) date, they occur twice on the same day.
If you have to schedule things in this period normally, then you need to think explicitly about what you do (if anything) on the day when no such time occurs and there are only 23 hours in that day.
And on the day when the hour occurs twice and the day therefore has 25 hours, you need to think explicitly about whether you run the job twice, or whether it runs only once (and if so, then whether it runs once in 0100-0159-a or once in 0100-0159-b).
I believe the Romans had a superstition about any timekeeping that was overly-regular, as it leads to civic activity being over-trained to a particular schedule, and a lack of consideration for how exceptional disruption will be handled.
Consider daylight-savings to be a similar innoculating practice, that not only challenges the idea that every day consists of 24 hours, but forces you to think about how a rare upset is actually handled!