Tiburcio began his professional career in the Dominican Summer League after signing with the Los Angeles Dodgers in 2020. The right-hander spent four years in the Minor Leagues and reached Low-A with Rancho Cucamonga. He held a 4.86 ERA in 133 innings pitched, striking out 111 while walking 58 during his time in the Dodgers system. At the start of 2025, Tiburcio signed with the New Jersey Jackals of the Frontier League, making six appearances and allowing two earned runs before being released and signing with the Bird Dawgs.