In 1904 he became master of the vessel. Rieber's tanker was bought by the three-year-old Texaco in 1905. After three more years at sea, he was given the job of building a terminal for Texaco at Bayonne, New Jersey. The terminal came into operation before it was complete, and the wooden buildings twice burned down. Rieber arranged for them to be quickly rebuilt. Rieber was then assigned to the company's head office. Rieber married Miriam Marbe in 1909. They had two children, a girl and a boy. Miriam died in 1938. During World War I (1914–1918) he was superintendent of terminals and assistant superintendent of the oil refinery at Port Arthur, Texas. The first boss of Texaco, Joseph Stephen Cullinan, fell out with Texaco's directors in 1913 and left to form another oil company, American Republics Corporation. After World War I ended, Rieber left Texaco and became a vice-president at Cullinan's new company. The company struggled to get organized, and in 1927 Rieber accepted an offer to return to Texaco as vice president in charge of exports and marine transportation. He acquired a fleet of new tankers and opened up markets around the world for Texaco. In 1929 and 1930 he tried unsuccessfully to reach an agreement with Heath Eves of the Anglo-Persian Oil Company (later to become British Petroleum) for the two companies to cooperate in Europe or other markets where BP did not have a partner. In 1935 he was appointed chairman of Texaco, with William Starling Sullivant Rodgers as president. Rieber featured on the cover of "Time magazine" on 4 May 1936. In the 1930s Texaco was the fourth largest oil company in the United States, after Standard Oil of New Jersey, Socony-Vacuum and Standard Oil of Indiana,  but relied completely on domestic oil fields. Rieber wanted other sources of supply in case the United States banned exports to one or all of Texaco's foreign customers. In 1936 Rieber bought the Barco oil concession in Colombia from Gulf Oil for $14,550,000, and sold a half interest to Socony-Vacuum, now Mobil. The crude oil had to be pumped over the Cordillera Oriental across a pass. From there the line ran west through the low-lying Magdalena River valley, in three places running under the river or one of its tributaries.