Plate-cultured bacterial colonies are intriguing models to study host-parasite interactions in senescent populations. During the growth of bacteriophage-infected colonies there is a synchronous prophage induction episode among lysogenic cells that allows a dramatic but time-restricted amplification of viral particles. We report here that the dynamics of phage spread depends on the history of the lysogenic cell that establishes the clonal population, the duration of the pre-burst period being shorter when the founder, infected cell derives from older colonies. These results offer a physiologic explanation for the self-contained progression of the viral spread in closed environments, that ensures both viral dissemination but also survival of most of the host cells.