Does The Last Samurai fit the modernization timeline?

Does The Last Samurai depict the right stage of Japan's military modernization?

Only partly. Its rebellion is closer to the later Satsuma revolt, while the basic modernization and training story would fit the Boshin War period better.

The film's rebellion belongs closer to the Satsuma Rebellion, which occurred after the Boshin War. By that later conflict, many government troops already possessed modern weapons, formal training, and recent combat experience. Foreign advisers could still contribute tactics and logistics, but they were not introducing an entirely unmodernized force to basic warfare. The scenario in which outsiders teach those fundamentals fits the Boshin War transition more naturally. The chronology separates a popular cinematic image from the sequence of Japan's actual military modernization.