And a regeneration can last up to 3 hrs until the vlave is back in the Service position but, water doesn't run for all that time. So maybe there isn't anything wrong.
When you say you turn off the softener to stop it, do you mean you put the by pass valve in the bypass position the water stops running (it's supposed to)?
If so, and when you put the bypass back in the Service position, and the water has stopped running, then that means you interrupted a regeneration before it was finished. And nothing is wrong but the time of day is allowing it to regenerate at a time other than 2 AM.
So describe what you actually do and in specific order.
BTW, you won't find this stuff in any manual.