Two different timelines. Also solves the "If I do this, my friend would never have been born"-dilemma as well.
Jack has been on a guilt trip for not returning to the past early on in the show so returning to it is going to happen. Probably the only twist on it is that Jack sends Ashi with the sword back in time, because if the time travel would reverse his non-aging curse, he would turn into a shriveled grandpa the moment he takes it and thus would be useless.
Either that, or he leaves Ashi to continue his legacy as he returns to the past. Ashi is an ideal candidate because she mirrors the future timeline itself, an abused victim turned violent but which still has a sliver of the beauty and good behind all the blackness.