While an engineering student in the Philippines Briones became involved with the original 1989 London production of Miss Saigon. Briones had a friend who was a Producer in the Philippines who asked Briones to help "facilitate an audition" for the Cameron Mackintosh team who were holding auditions in the Philippines for Miss Saigon. In addition to helping with the organization of the auditions, Briones himself auditioned for and then became a member of the ensemble.
He has been involved with various touring productions of Miss Saigon, as a swing and covering other roles, finally playing the Engineer. In 2014 he joined the original cast of the Miss Saigon West End revival, playing the Engineer. He was nominated for the Laurence Olivier Award for Best Actor in a Musical for playing this role and won the Whatsonstage.com Award for Best Actor in a Musical. He remained in the role until the production closed on February 27, 2016.
In 2017, Briones transferred with the production to Broadway at the Broadway Theatre. Previews started on March 1, 2017, with an official opening on March 23.
In 2018, he appeared in The Assassination of Gianni Versace: American Crime Story, as Modesto Cunanan, father of Versace’s murderer, Andrew Cunanan.
