I just finished reading Kanan the last padawan 1, and something just occurred to me. Did Palpatine personally call every clone trooper commander and tell them to execute the order? He says in this issue. "Commander Grey, the time has come. Execute Order 66". Those are his exact words to Commander Cody, with only instead of Commander Grey, he said Commander Cody. Did Palpatine personally send a holographic transmission to everyone, or did he just broadcast one that made an automatic call to the other troopers, addressing them with their first name and the same message?
Palpatine probably just personally ordered the executions of those on the High Council or th jedi of some repute. Commanders of the average jedi that weren't particularly well known (Dass Jennir, Beyghor Sahdett, Kai Hudorra etc.) most likely got a prerecorded transmission of something.
Honestly it would be impossible to contact all the clone commanders of 6000-10,000 jedi in such a short time.