We numerically investigated the gravitational collapse of a rapidly rotating massive star and the subsequent propagation of relativistic jets, varying the timing of jet injection. In this study, we pay particular attention to observational consequences of the difference in the timing of jet injection. In order to discuss them, the light curve of photospheric emissions is also calculated by the post process. In calculating optical depths to find the location of the photosphere, we take into account the relativistic effect such as the time retardation accurately. We find that, as a consequence of rotating massive star collapse, the centrifugal shock wave (CSW) is formed, then it propagates outwards and breaks out of the envelope into the stellar wind. Which of the jet and CSW breaks out earlier depends on the timing of jet injection. If the CSW breakout occurs first owing to later jet injection, the jet propagation and subsequent photospheric emissions are affected substantially.