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.
Tarkin still orders the destruction, Vader is just the one who tells them to release the primary ignition.
He’s the link to the script: https://imsdb.com/scripts/Star-Wars-A-New-Hope.html