Tiyua was born as a member of the Kakwa people in Maracha District, part of the West Nile Province of Uganda. He joined the Uganda Army in 1961, and was lieutenant by 1971. When Army commander Idi Amin ousted President Milton Obote in the 1971 coup d'état and installed himself as dictator, Tiyua remained in the military. Tiyua considered it his duty to obey the Commander-in-Chief, and thus did not question Amin's dictatorship. By 1977, he had risen to lieutenant colonel and commanded the 2nd Infantry Battalion, better known as Gondo Battalion, stationed in Moroto.