You're measuring the temperature of the swamp cooler water and not the beer, and the beer will take a long time to reach the cooler water temperature, which will also rise in temp during the same period. This is because heat transfer between the beer and the cooling water is slow, since the surface area is small compared to the volume, plus both liquids are not in motion.
So, what I expect will happen is that the beer temp will drop in a few hours, but no where near the drop from 75F to 60F. Probably somewhere in the middle - 66-68F at a guess. So I think the yeast will be fine.
But what would happen if you really did drop the temp to 60F? The yeast would drop out of the beer and stop fermenting, leaving a high FG/low attenuated beer.
After the first 3-5 days of fermentation (depending upon activity level) it's a good idea to slowly raise the temp of the beer to 72-74F so that the yeast are encouraged to continue fermenting and not drop out. This will give you a better attenuated beer that often requires less conditioning time. The increased temperature doesn't give the off-flavours you mentioned, since the bulk of fermentation is now complete - the yeast are much less active and produce far fewer flavor compounds.
EDIT: As you see, Denny and I have different perspectives, and unless you have a probe immersed in the beer, you don't really know what the fermentation temperature is. While one yeast strain may tolerate a drop to 60F or lower, another may stall at that temperature. Either way, it's not usually a crisis, just rouse the yeast and raise the temp and fermentation will typically pick up again. But ideally you should be looking for a more even temperature - avoid temperature swings. You can try adding just a single bottle more frequently, rather than dumping 5 in at once.