Hint: They did have power tools - at least at the Colt factory. They were run by overhead belts, that in turn were powered by a central steam engine.
But you have a good point. If you review contemporary literature from the middle 19th century you will find occasional references to cap fragments jamming a revolver, but the problem wasn't common. Obviously the military services of the time couldn't tolerate a situation where guns constantly got jammed up at a critical time.
Also keep in mind that during those days C&B revolvers were the only kind there were. Metallic cartridges hadn’t been invented yet, so the use of these guns was universal, and the problem had a much greater opportunity to happen.
So why didn’t it?
The answer largely is because the lockwork was adjusted so that the cylinder would start rotating almost immediately after the hammer moved backward, leaving too small an area for the cap to fall in. Also the fired caps tended to split, but not fragment; and shooters would often tip the revolver to the side, or hold it over their shoulder up-side down while they cocked it.
And yes, fixing the timing is something you can do with hand tools.