Warm air rises. In a forced air incubator the fan keeps the air stirred up so the temperature should be the same throughout. That may not always work in some incubators or a homemade one, but in the good ones it works pretty well.
In a still air incubator it's important at what elevation you take the temperature. The normal recommendation is 101.5 F taken at the top of the eggs.
I don't trust any thermometer unless it has been calibrated. Were those three thermometers calibrated? Were they all at the same elevation?
The older and larger the embryos get the more they generate their own heat. To start with there isn't enough living mass to generate much heat but the closer you get to hatch the more heat they generate. If those eggs were in there less than two weeks they are not going to generate any noticeable heat.
The way the incubator is supposed to work, the heater comes on when the temperature drops below a certain level and then goes off when it warms up to a certain level. This is usually set at a very tight difference so it can cycle a lot. If something else light living body mass or a turner motor generates additional heat then it may take a slightly longer time for the thermostat to cycle. But the thermostat and thermometers are not going to be in exactly the same place. Depending on that placement you might see some differences.
In commercial hatcheries where they may have 60,000 or even 120,000 eggs in one incubator this generated heat is a big issue. They have to get the heat out of the middle of the incubator or hatcher so it doesn't cook the nearby eggs. Our incubators are not packed that tightly so it's not really an issue for us.
I don't know why your incubator spiked like that if it really did. I don't have any suggestions other than to take the temperature in a still air where you should and use calibrated thermometers.