When he was then asked if he wanted to kill the puppy or be put back together and agreed he would do as ordered, was his experience of being restored completely on the spot merely the undoing of an illusion of a wound in the first place, or was he taken back in time to restart the sequence with an intact body but with a memory of what happened in between to motivate him?

The latter is the case, as you saw intuitively. This was a real event in every detail, that he was in this position, it was a real puppy he was ordered to kill, and he had a lethal weapon in hand so the means were there. What was lacking was his willingness. So, to train him further and manipulate him further, he was given an object lesson along with some mind alteration instructions by causing a grievous and fatal injury of excruciating pain, and was then re-ordered to choose to obey or be restored to rescue him, and chose the lesser of evils at that point being willing to kill an animal to save his own life. This immediately was followed by restoration of the body through a time travel capability the Reptilians are adept in carrying out. It is simple for them to cycle back in short spans of time or long, and to then have a replay in order to gain further experience or change the direction of what takes place. So this allowed the trainee to have a second chance to obey the order given him and avoid the personal demise in a ghastly and painful way.