Well, not always. It can vary by a day or a few hours either way. Temps can affect how fast chicks develop too. Too high or low can cause them to be a day late or a day early. What time you set them counts too. If you put the eggs in at 5pm October 1st, you wouldnt really call Oct. 1st 'day 1', since 24 hours hadnt passed yet, you could call day one Oct 2nd at 5pm.
There arent many 'exacts' when it comes to chickens. Age they lay will vary, how disease resistant will vary, lifespan will vary, and egg hatching time will also vary (but not as much.) It is usually 21 days, but I've had pips on day 21, and a whole hatch on day 22, and I've had hatches on day 20, but usually very late at night on day 20.
First, can we define 21 days? An egg does not have 24 hours worth of development 2 seconds after it has been put in the incubator or under a hen. It takes 24 hours for an egg to have 24 hours worth of development. Instead of talking about day this or day that, I prefer to think of it as days of development. An egg has had 8 days of development after it has been incubated for a full 8 days, not 7 days and 2 seconds. As an example, if you put your chicken eggs in the incubator at 7:00 p.m. on Thursday October 7 and you want to candle them on day 8, you should candle them around 7:00 p.m. on Friday October 15. If you want to go into lockdown after 18 days of development, you should lock them down around 7:00 p.m. on Monday October 25. I know the original poster is not using an incubator, but this is for general information. Hopefully that is OK. Expected hatch time should be Thursday October 28. The easy way to remember if you are hatching chicken eggs is that they should hatch on the same day of the week as you set them. In this case, set on a Thursday and hatch on a Thursday.
Is it always 21 days for chickens? No, it is not. It depends a lot on the average incubating temperature. Even with a hen, the average incubating temperature can be off the perfect temperature by a bit, depending on climate, how well the nest is insulated, and how long and how often her breaks are. If the average incubating temperature is high, they will be early. If it is low, they will be a bit late. I read a paper, I think University of Virginia but not sure, that said genetics can influence if a chicken hatches early or late. How the eggs are stored can influence it too. If the eggs are stored at a fairly high temperature they can develop a bit before they go under the hen or in the incubator so they could be a bit early. There are probably some factors I'm unaware of, but no, it is not always right at 21 days, even with a hen.
Hatching is not an instantaneous process. The chick positions itself for hatch. It pips. That is such hard work it has to rest, often for many hours. It zips. Usually it pushes the shell apart fairly soon after it finishes zipping, but not always. That is such hard work, it usually has to rest for a while. After a while it is up drying off and moving around. If it is in an incubator it plays soccer with the eggs that have not yet hatched. If it is under a hen, it moves around, sometimes peaking out or even moving out from under her, but going back under when it needs to.
I'm not sure if this answered your question or not but I hope it helps. Good luck.