The emergence of propagating pulses was investigated with the photosensitive ferroin-bromate-pyrocatechol reaction in capillary tubes, in which various interesting spatiotemporal behaviors such as propagation failure, breathing fronts, and transitions between propagating pulses and fronts have been observed. Rather than a mutual annihilation, the collision of a propagating pulse and a growing front forces the front to recede gradually. A phase diagram in the pyrocatechol-bromate concentration space shows that the pulse instabilities take place throughout the conditions at which the system generates wave activities, suggesting that the presence of coupled autocatalytic feedbacks may facilitate the onset of pulse instabilities.