I'm just guessing as wildly as Doc Brown's hair, but it seems logical that the "white" fat is the storage form of fat, while the brown one is the kind that body uses to do actual useful stuff. Like in a gasoline engine -- the gas is stored in concentrated form, but it's diffused and mixed with air moments before the actual combustion, as that's more efficient.

So body creates the exercise-fat to have a ready source of energy required for physical activity (remember, while humans were evolving there were no exercise, only physical activity needed to survive).