The term itself originated in the First World War, and it's origins likely stem from the infamous 'Hun Address' given by Kaiser Wilhelm II to German soldiers leaving to help crush the Boxer Rebellion in 1901. The Kaiser encouraged the soldiers to, roughly, 'establish for Germany in China a reputation the likes of which Atilla's Huns enjoyed in Ancient times.'

To my knowledge they followed up on his wishes when they reached Peking. The conduct of German soldiers in Southwest Africa, East Africa, and Kamerun was likewise brutal; the conduct of the German Army in Belgium and eastern France probably sealed the deal.