In the shooting script, Darth Vader is the one who orders the Death Star technicians to “Release primary ignitions”, thus making him more directly responsible for Alderaan. I wonder why this was changed.
Yet another serendipitous thing that presciently paved the way for Vader to become Anakin Skywalker.
My guess is they changed it because Tarkin dies when the Death Star explodes, but Vader survives. Thus, there is more “poetic justice” if Tarkin was the one who ordered the destruction of Alderaan.