I don't think you can tell for sure from this description whether the scavenger hunt will be during or after the race. What I CAN tell you is that last October I ran the final Tower of Terror 13K race. It was a night-time race which was neat, and they announced there would be a mystery to solve during the race. I wasn't sure how they would arrange this, but I wasn't impressed. At the start of the race and at each mile marker was a clue as to the identity of a so-called killer. On our racing bibs were the names of all the potential killers with a place to pop out a hole if you had eliminated someone as a possibility. I am not a fast runner by any means, and I had no illusions of winning this race, but I still found it impossible to figure out all the clues, punch holes out of my bib, and run the race at a constant pace at the same time. I thought it was very lame. I was glad I ran the race just for the experience of running a race at Disney (that just happened to fall during our vacation!) and to be able to have free reign of DHS after the race, but the Mystery Tour during the race was silly.
My point in telling you this is that I don't think you should assume that the scavenger hunt will be AFTER the race. It may very well be during the race. I think that the obstacle course and scavenger hunt sounds much more cool than our silly mystery tour. I hope you enjoy the race, but if you plan to do all the activities they offer during it, plan on doing less actual racing, and just enjoy it for the experience. Also, another note, the 13K course was VERY crowded and narrow for the first 3 miles or so (at least for slower runners), so I would imagine that the entire 5K race course will be rather crowded.
Again, I have no definitive information for you, so maybe someone else can be more helpful. These were just my impressions of my Disney race last Fall.
Jill