It was only in the army that the Romans counted time, the night was divided into four watches and the guard was changed at the end of each watch. So when you read latin text, it states it by like this id est " on the third watch." I can't remember the exact time they divided into, just that they made the day into four parts.
The Romans most probably used a horologium wherever they went. They just considered it as day and night, but the army is different as I mentioned.
Most importantly, time only mattered to the Legions.
Wait nvm, now I remember. It was the night that was divided into four watches, from sunset to sunrise, was divided into four watches (vigiliae), numbered prima(on the first watch), ending at 9:00 pm; secunda(on the second watch, ending at midnight(12am); tertia(on the third watch), from midnight to 3 A.M.; and quarta(on the fourth watch), from
3am to sunrise. In the earlier times, and probably in Caesar's army, the password of the sentinels, different each night, was written on slips of wood, which were given by the commander to the military tribunes, and passed by these to the men on duty.
This is a good link on what you want to find.