The main difference is that if salvation is cast when the spell is cast, then you will know immediately if the spell has worked or not. You can then use this information to inform your decisions for the rest of your shift. For example, if he issued the "stop" command and knew that the target failed his salvation, then he knows that he does not need to leave the target's melee range in this round, as they will not be able to attack him. . In contrast, if salvation moves in the target's turn, he does not know what the result is until his turn ends, so he must consider both success and failure when taking the rest of his turn.
There are also other minor mechanical implications, such as giving other characters a window to affect the outcome of the roll (as noted in Luke's response), but the difference in information that you have on your turn is the main distinction. since it will be relevant every time you cast the spell.