In the PDf version P110 it says that :
a Professional general is replaced at the movement phase
An instinctive general is replaced at the end of the turn.
If killed in melee /combat phase :
The professional appears at the next turn at the movement phase
The instictive appears at the end of the current turn
Is that correct ?
Don't forget the bit that says:
"Unless there are no UGs left in the command, a replacement general will take over in the turn after the general dies,"
My emphasis.
So no general can be replaced in the same turn as they die in.