Julmis began his refereeing career in 2017, while still attending CR Walker High School in Nassau. He played for a local school team at the competitions organized by the Government Secondary Schools Sports Association, and was also a member of the Nassau-based soccer team Dynamos FC.[1]
By the age of 22 in May 2022, Julmis got his first CONCACAF appointment when he was selected as a fourth official for the 2022–23 CONCACAF Nations League B game between Haiti and Bermuda, played on 4 June 2022 at the Bermuda National Stadium in Devonshire Parish.[1]
FIFA listed Julmis in its 2025 roster, with Julmis being the only Bahamian central referee at the level.[3] In January 2025, he was selected for a training program and seminar in Costa Rica, as part of CONCACAF requirements for further tournaments, including the CONCACAF Gold Cup and the CONCACAF Champions Cup.[4] After the seminar, Julmis was appointed to referee matches at the CONCACAF U-17 World Cup qualification, including a match between Saint Kitts and Nevis U-17 and the United States U-17 in Costa Rica.[5]
Prior to becoming a professional referee, Julmis was part of the Bahamian national team, as well as part of the beach soccer squad.[1]