As you can see, there is some disagreement on how to count. The real problem is when to start. Timing does start when they go into the incubator. No question about that. I personally don't like counting day 1, day 8, day 18 and such. I think the terminology should be days of development instead of day this or that to help get rid of the confusion. The way I look at it, an egg does not have 24 hours worth of development one second after it is put in the incubator. It has to develop 24 hours before it has 24 hours worth of development. If you are going to candle the eggs, you should look at the pictures for how many days it has developed to see what the pictures should look like. For example, if you are going to use the pictures for 8 days of development, you should candle the eggs after 8 full days of development, not 7 days and 1 second. Lockdown should be after 18 days of development, not 17 days and 1 second. So a chicken egg that is put in the incubator at 8:00 a.m. on the 1st has one day of development at 8:00 a.m. on the second. 18 full days of development will have passed at 8:00 a.m. on the 19th. Hatch should be at 8:00 a.m. on the 22nd. It will almost never be exact, but that is the time you should shoot for. I also do not think the exact timing of lockdown is that critical. The two things you do at lockdown is up the humidity and stop the turning. I think the two are related in that they are both directed at stopping the chick from sticking to the shell or membrane, so as long as you do them both together, it doesn't matter that much if you are several hours early or late. As a matter of good practice, I try to go into lockdown pretty close to 18 days of development but I'm not sure it is that critical to hit it exactly.
Hatching is not an instantaneous process. The chick pips, then rests, sometimes for many hours. Then it zips. Usually it pops out of the shell pretty soon after completing the zip, but sometimes it rests a bit first. They do not all hatch at exactly the same time either. Some eggs hatch earlier or later than others, even if the conditions have been about the same during incubation.
Some of the things that I know of that may affect when an egg will hatch. If the incubation temperature is a little high, the hatch will be early. I've had them hatch two days early in an incubator because of this. If the incubation temperature is a little low, they will hatch late.
How you store the eggs before incubation can have an effect. If the storage temperature is high, the eggs can partially develop and they can hatch earlier than expected.
The size of the egg makes a difference. I've read that smaller eggs will hatch earlier than larger eggs. I don't know if this means that eggs from breeds that lay smaller eggs will hatch faster than eggs from breeds that lay larger eggs or if they mean that the smaller eggs from the same breed will hatch faster than larger eggs from the same breed. They just say smaller and don't explain it.
I've seen a paper (I think from the University of Virginia but I have not been able to relocate it) that said some chickens are genetically programmed to hatch earlier or later than others.
My broody this past summer when it was in the upper 90's spent a lot of time off the nest hob-knobbing with her buddies, but on coooler days, she spent more time on the nest. I assume her instincts told her with those air temperatures she did not need to be on the nest as much.
Kelly G, I don't think I have addressed you question exactly. I am not aware of any better or worse time to start the eggs. I've had about the same hatch rates whether I start them in the morning or the evening.