I went into the rules on cartridges and couldn't help, but notice that metal cartridges are considered alchemical.
Pg 141 of Ultimate Combat
Metal Cartridge: These sturdier versions of alchemical cartridges serve as the ammunition for advance firearms. They can hold either bullets or pellets.
Now with that being said, is it not applicable to the Revolver to use such rounds, as it is what they use. If metal cartridges are considered to be alchemical that would show that a revolver with rapid reload and alchemical cartridges would be a "free action" to reload.