Perfect sense, although given that I was only off by a couple degrees, I probably could have just taken it off the heat and let it sit for two minutes to cool before adding it to the grain. By the time I got the chiller hooked up, I probably would have already lost too much temp. As I get more experience, I would also expect to have a much better idea of *how much* cool water to add to a mash to get the temp down a couple degrees, rather than overdoing it. It wasn't like I was ever out of range, I just started too far on the high end.
Plus, I now have a better understanding of how to use tools like BeerSmith, so I can get a more precise measurement of how how my mash water need to be to hit my target.