The specials are basically snippets of their past lives. The main timeline, .i.e the main story is set in modern times (aka our time) and their present selves are reincarnations of their past selves.
This should be their first reincarnation of Hosik and his Hyung after Hosik dies of illness in the first life where they were a personal servant and noble respectively. (aka Feudal period) This was also before Japan colonised Korea. Anywhere before 1900.
(Current update) Presumably Hyung reincarnated in a descendant of his noble life's son and Hosik here is most definitely a North Korean refugee who fled south. So this particular timeline is set after the war, it could've have been during the Korean war itself but given the peaceful setting and the industrial revolution, I'm leaning on towards after the war, so it's set anywhere between late 1950s and 1970s.
can someone explain what is happening and how the specials connect to the main story pls