In addition to the other information, it is not at all unusual for eggs to hatch a couple of days early or late, whether in an incubator or under a broody. I've had eggs pipping when I went into lockdown. I've had eggs hatch two full days early under a broody. I think with mine that is mainly a combination of heredity and incubation temperature. It could have other things affecting it.
Are you sure you are counting the days right? It's not at all uncommon for people to miss it by a whole day. There is even a hatching calendar on this forum that has it wrong.
Eggs do not have a day's worth of development 2 seconds or 2 hours after you put them in the incubator. It takes 24 hours for them to have a day's worth of development. When you count the days, think of it as days of development. If you set them on a Monday, Day 1 of development is about that time of day on Tuesday. An easy way to see if you are counting the days right is that the day of the week you set them is the day of the week they should hatch. If you set chicken eggs on a Monday, they should hatch on a Monday.
Remember that this is just a rough target. Actual hatch could be off by a couple of days. Also remember that lockdown does not have to be real precise. Several people use that bogus hatching calendar and lock down a day early and still get pretty good hatches. Think of it as a guideline, not an absolute law of nature.
I'm not too worried about temperature fluctuations when opening an incubator. The core temperature of the eggs is what is important, not the air temperature. It takes a long time for the core temperature of the eggs to react to temperature fluctuations. Too much heat is worse than not enough also. Cooling off a little won't bother them.
The risk of opening the incubator during lockdown is in possibly shrink-wrapping the chick. This is where the membrane around the chick dries out enough to shrink around the chick so tightly it cannot move to pip or zip. Until it pips there is no real risk of this happening just from opening the incubator. That membrane is just not going to dry out that much in those circumstances. It can happen if the average humidity is too low during incubation but not from an instantaneous opening the incubator. That shell does too good a job of protecting the chick.
Even after the chick has pipped, you probably will not shrink wrap each and every chick that has pipped if you open the incubator. There is a huge difference in what can possibly happen and what will happen each and every time. It can happen so it is best to not open the incubator when one has pipped, but that is not necessarily a death sentence to each and every egg if you do open it. Sometimes eggs pip on the bottom where you cannot see the pip.
I have opened the incubator after eggs have pipped. For instance when the eggs had pipped before lockdown. Usually they hatch without a problem. But I also have shrink-wrapped a couple doing that. If I have a reason to open the incubator during lockdown, I will. But I understand the risk and have to have a real reason, not just I want to cuddle a chick.
Before they hatch they absorb the yolk. They can live at least three days after hatch without eating or drinking after hatch because of that. I generally don’t open the incubator after lockdown until the hatch is over. If I need to add water, I use this, going in through a vent hole.
Hope this helps. Good luck.