We come to the second reported trip to the past, and already we have two inconsistencies when compared to the first.
On Tim's first trip to the past, he went into a closet, traveled back a matter of hours, and emerged from the closet in the past. He then did what he wished, re-entered the closet, and traveled back to the future, emerging again from the closet.
The second trip is inspired by Charlotte, the cute girl spending the summer with Kit. She asks Tim to put suntan lotion on her back, and he spills it, so he runs away to go back a few minutes and fix the problem. We do not see him enter the closet, but assume that is where he goes; however, he does not exit from the closet. Rather, he simply appears as himself where he was at the moment he has targeted.
This is more consistent with the Butterfly Effect/Quantum Leap concept of time travel, and our objections to it have already been voiced (concerning what memories each version of the time traveler has of the events). The problem here is that it is inconsistent. We do not always see his departures and arrivals, but we do see other arrivals for which he remains in the closet while traveling to the past. With this one, when he becomes his previous self he does so where his previous self was. This creates fewer problems in one sense--after all, if we are to assume that on the first trip Tim replaced himself at the party, how did his doppelganger wind up in the closet, and did someone see him vanish from the party to get there? Having Tim take over his self wherever he was at the time is in some ways less problematic as a time travel method. The objection is not that it was done that way, but that it was done that way only sometimes, and done differently other times.
The other inconsistency is less problematic; it only demonstrates an aspect of the process that might not have been anticipated. This time he does not return to the future--he simply lives through those moments again, doing it right the second time through, and stays with the timeline. It makes sense for him to do it that way this time, because it is a very short time, the time of his original departure probably arriving before he is finished with the correction. It will matter, though, in later situations.