Gee whiz, all over movie trivia....
You're the only one that seems to be getting their panties in a twist, fella.
On your 51 navy rig, the tin lined box is an ammo box for rifle/carbine ammo. It even has the tin liner like most variations of the era. You see, that other box on that belt is a military ammo box made specifically to carry packaged paper or foil cartridges for revolvers.
As OJW pointed out, the revolver was not the primary weapon. Just because a cylinder fits into the box, doesn't mean that's what it was made for. You know what they say about ass-umptions. As for cased sets with spare cylinders, as Hawg said few and far between. Most cased sets with extra cylinders that I have seen were Colt Paterson revolvers. How many "regular" cowboys, shop owners, lawmen etc. do you think carried (or could afford) a cased set revolver? These were mainly presentation grade guns. Given to heads of state, military officers, entertainers etc. Most were engraved and/or had custom grips. These were not the guns of the "working man". And few had "spare" cylinders. If as you say, spare cylinders were used during the civil war, westward expansion etc., why do you not see dug up relic "spare" cylinders in civil war museums alongside the dug up relic revolvers? Just something to think about.