There is a description of time keeping in one of the OR CD preambles which I cannot access anymore.

However, they note that time at any location was determined by the sun's position at it's highest, that being noon.

Railroad companies kept the time of their headquarters.

I have a description of Lt. Col. Key of the 43rd Tennessee who made a trip to Richmond from Knoxville switching railroads at Bristol, Tenn./Va.

Starting out at Knoxville on the East Tennessee line, he planed to be at Bristol by 7 PM to catch the Richmond 7:30 train on the Virginia line. As they were arriving in Bristol he was dismayed to see the Richmond train departing. How so, well, it seems that when the sun passed over Richmond at noon, it wouldn't see high noon in Knoxville for 30 more minutes. Hence, the Virginia line time was 30 minutes ahead of the Tennessee lines time.

Thus Key had to cool his heels for another 24 hours!