Another thing that happens too is the thermostat probes will take a bit longer to warm or read temp as well. Like how a thermometer under your tongue takes a bit to give you the final temp.
So while the probe is catching up to the temp of the heat tape there will be that bit of variance. As said above, being placed between the tub and the tape will vary the measurements as well. It keeps them a bit more even with what you are hoping for as it will stay a more even temp than in open air.
It's okay that the heat tape gives small spurts of higher temps as long as it doesn't seem to be damaged or damaging something else. This is why you can't just set and forget. You do need to check your enclosure temps regularly as well.
I actually purchased a rack system from someone recently where everything was fine except for the very last foot of heat tape.... Which burned a hole in the tub. Thankfully the animal wasn't injured. The owner had a digital temp sensor attached that would give him temp updates, but the sensor was for the ambient air and not the heat tape itself.
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