I think the time-line is off, but there seems to be an attempt within the movie to skip past a time period in which the chief character is recovering from his wound - which could have been months or more than a year. It seems that the concensus (on-line, at least) is that the battle scene is complete fiction, so nailing down that part of the time-line would be like trying to hit a black kit with a stick in a dark room, blindfolded.
As for the time-line of the repeating rifles, those with more knowledge of ACW and "Old West" weaponry can surely provide the details of which repeating rifles were available, and when. The Winchester seems to be a newer repeating rifle than that which would have been available during the ACW or shortly thereafter, although other repeating rifles were available.
It also seems, that the chief character made the transition from infantry to cavalry somewhere along the line - which might explain the access to repeating rifles earlier than would be expected of the infantry?
But remember - it's just a piece of fiction. Take it for what it's worth, and try to enjoy the movie without getting hung up on uniforms, weaponry, etc.