I'm sure it wouldn't have any effect. The Death Star is, what, 160 km across? It's unlikely to cause any disruption whatsoever to the planet. Our moon is approx 2,500 miles across and phenomenally heavier than the Death Star and that doesn't create massive tidal pull. Sure, it is the major factor in our oceans, but the lunar tidal pull is not at all violent, relative to other such influences in planetary systems. So the Death Star is unlikely to have any noticeable effect, and even less given the very short amount of time it's near Alderaan.