I wouldn't say it continues to cook, but it does still keep the food warm, which is a great benefit and selling point. This is how I explain stoneware works in the oven: since ovens run with a thermostat, the temperature fluctuates throughout cooking. If the oven senses that it's not quite 350 degrees, it'll kick on and compensate for that. If it gets over the set temp then it'll turn back off. So, it's really never a constant temp. The nice thing about stoneware is that once it gets to the desired temp, it stays there. The food cooks/bakes much more evenly and thoroughly. Then when you take it out of the oven, the stone SLOWLY cools, but still stays warm and keeps food warm too. Since it no longer has the heating element of the oven it really doesn't continue to cook.

Hope that makes sense!