Preheat and baking temperature
After opening the door the temperature is supposed to drop a few degrees since it's exchanging heat with the outside air (which is usually colder than in the oven...).

The cake batter should also absorb part of the heat put out by the oven, by heat transfer. So if your oven is very small (like an oven-toaster-grill), weak, leaking large amounts of heat (through openings or cracks) or you're putting a huge amount of really cold cake batter the temperature might not rise back to previous levels.

So I'd say it's not normal - at least I never saw such a large temperature drop for such a long time. Trying bake a smaller cake, or checking that the baked goods are not blocking the heating element or the air circulation inside the oven.

Try also putting your thermometer in a different position inside the oven and see what's the difference - maybe just part of the oven is not getting up to temp, since you said your cakes are baking fine.