Tulbagh was the son of Dirk Tulbagh and Catharina Cattepoel, who moved their family to Bergen op Zoom when Rijk was still an infant. There he attended the Latin school. As a 16-year-old he enlisted with the Dutch East India Company and in 1716 sailed as a cadet on the ship Huys Terhorst to South Africa. His career with the Company advanced rapidly. He was appointed a temporary assistant to the Council of Policy in 1716 and he received a full appointment in 1718. In 1723 he became chief clerk and later in the same year book-keeper. In 1725 he rose to become secretary to the Council of Policy and in 1726 to Junior Merchant. In 1732 he became a merchant. In 1739 he became Secunde (the second highest administrative post) and 27 February 1751 he was appointed Governor.
In 1725 Tulbagh married Elizabeth Swellengrebel, the sister of Hendrik Swellengrebel, Governor of the Cape Colony at the time. She died in 1753. Tulbagh himself died in 1771 and was buried in the Groote Kerk in the grave of his wife and father-in-law.