Preheating oven increases temperature?

Sadly, yes.

Your oven most likely has been running too hot for a while and now that you are actually measuring it, you noticed it.

We have a lot of Q/As on the site that recommend using a separate oven thermometer whenever an oven behaves strangely. Thermostats can fail or be generally incorrect, like too hot or too cool. Plus many ovens fluctuate quite a bit.

If you noticed that your recipes didn’t turn out the way you expected or were used to, getting that oven thermometer was a smart move. Either adjust the temperature to the desired value, if possible (and note down what setting that corresponds to), or consider having the oven serviced or repaired. In some models, the temperature knob can be adjusted, which would be a super trivial thing and may even explain why the oven is set to a wrong temperature.

If your question was wondering more about the still rising temperature - ten minutes preheat is on the shorter end of preheat time, especially for old ovens. You can be dealing with quite a bit of thermal mass.

It is entirely possible that your oven runs hot, many ovens do. But right now, you cannot say anything about it. A single temperature measurement at the tenth minute is a pretty useless piece of information.

What your oven does is to turn its heater full-blast on, then off, in a predetermined pattern (the whole time, the oven indicates that it is "turned on", that's normal, I'm speaking of the heater inside). The temperature knob determines the ratio of time the heater is on vs. off. This means that the temperature will oscilate a lot in the beginning, meaning that the temperature is quite hot while the heater is on, and quite cold when the heater is off. With time, the oven is supposed to get properly preheated - that means that the whole heavy iron mass of it gets hot, and starts steadily radiating energy into the cavity. With a properly preheated oven, the food isn't getting cooked as much from conduction from the hot air, as from radiation from the oven walls. The heater still goes on and off, but in a smaller amplitude, and its effect is anyway "overtaken" by the effect of the oven's thermal mass.

You may be thinking that you have preheated your oven, but you certainly haven't given it enough time for that "proper preheating" I have described. While it is impossible to define an exact moment when it happens, it takes at least an hour, preferably longer. At the tenth minute, your oven walls are still quite cold, and what you measure is just one random point in the oscilating heating cycle.

This doesn't mean that you cannot use your oven after ten minutes, you just have to be aware that at this point, it is acting more like a toaster oven than like a classic oven. The temperature is even less precise than in a classic oven, and changes quite erratically. Luckily, most foods can tolerate that reasonably well.

If you are bothered that maybe your oven runs hot in general (that is, that the steady-state temperature it reaches after a proper preheating is higher than what the knob shows), then you should preheat it for a long time, maybe two hours to be on the safe side, and preferably with some added thermal mass like a pizza stone, then take a series of readings without opening the door. If it turns out to be hotter than the set temperature then, you can start calibrating.