A cup of coffee doesn’t have 390mg of caffeine, but a cup of the charged lemonade doesn’t either. The 390mg figure is for a large, which is 30 ounces, equivalent to about 4 cups of coffee, which is in the same general ballpark for caffeine content depending on the type of coffee and how it is brewed.
They’re using the 390mg figure because it sounds scary without putting it directly into context. They are relying on the reader not doing any math to see of that is actually an outrageous number which it isn’t.