What the modern age of time keeping brought, i.e. trains etc, was time zones. Prior to that, it was always local time; which was set to 12 o'clock noon, which is easy with a sun dial, i.e. the 12 noon sun dial was the "time standard" everywhere.
Any variance from that local standard is simply the time accuracy of each individual time piece and the skills of the timekeeper. The history of keeping track of time is completely separated from the history of war. Whatever was the premier method of keeping time, at the time of whatever event you are interested in, is the general accuracy of the "true" time reported. I would expect that there would be in any army at any point in time any number of individuals who would be expert in keeping time: it's a natural human activity.
The wide variance seen in the reported time of events is certainly the usual variance in human reporting; which, in general, is not so good. So, what you are seeing is the variably of people, not the variably of the method of keeping time.