The answer to this question can vary depending on how much you use the hot tub as if it is covered a lot of the time then it might be the best idea to drain the water before refilling it again and using the ozonator. Constantly using the ozonator when there is no need too is just going to be a waste of energy and speeds up the time you’d need to replace or repair the device.
If you are using your hot tub often though then you are looking at running it for around three hours for every half-day of use. If you’re using the tub then it makes sense to keep it on to make sure that the water is staying clean. If you’re going to be using the hot tub for the whole day then it’s probably for the best to just keep the ozonator on for the whole day.
You might want to still use a small amount of chemicals which will make sure that the water is clear as these will work with the ozonator while it’s cleaning your hot tub. It’s best to err on the side of caution though and to leave the ozonator on for longer if you are ever unsure about how much you should be using it.