Anthony may have survived the fire as a baby, but the Candyman would go on to haunt his very life years later. The Candyman originally chose to sacrifice Helen, the protagonist from the 1992 film, and Anthony so that his legend could go on. However, Helen saved baby Anthony before stabbing the Candyman.
Towards the end of the movie, Anthony discovers that his mother has lied to him about his birthplace and when he confronts her about it she reveals a secret: he was the baby that was saved from the Candyman by Helen Lyle all those years ago.