Then if you eat a complex carb food that has 50 grams of carbs, it will be broken down over a period of time, such as 10 grams an hour and your body will simultaneously be using the glucose as energy in the mean time so there isn't a build up of sugar in your body that can cause acne.
But, the real culprit is unstable blood sugar levels.
Now, it is true that eating simple carbohydrates increases blood sugar levels. And refined carbohydrates trigger even sharper increase. But the body is very good at regulating blood sugar levels. It has to, because too high or low levels are dangerous, and possibly even fatal.