It is 1/3 cup dry, unless it specifically says "cooked" or "as prepared" on the label. Food manufacturers are generally required to give the calories for food as it comes out of the package, without any preparation. They can include the calories for the food as prepared according to their directions, but this is usually an additional column on the label and they have to specifically say that it is "as prepared."
Also, I'm a big oatmeal fan as well so I happen to know that 1/2 cup dry usually works out to about a cup of oatmeal prepared and is 150 calories. So 120 calories for 1/3 cup dry sounds about right or even a little high. 120 calories would be really high for 1/3 cup of cooked oatmeal (and that sure wouldn't be very much oatmeal to eat
).
It's possible that the website you are looking at is also giving the calories for dry oatmeal or it is just wrong. According to calorieking.com, 200g of cooked oatmeal (which is about how much cooked oatmeal you are ending up with) is 126 calories.