From what I understand, the leveling happens to -you- rather than your character, and your character takes on that level and when it dies, your next one takes on the level, which seems kind of weird to me, though it is understandable in combating the hardcore stigma of permadeath. But the weirdness is that it is kind of like being possessed by a ghost or something and then becoming super competent.
Its just my opinion, but it would seem less weird (IE, more in line with the theme of the game) if individual character leveling was individual, but your overall level was the level of the towns you've controlled and developed, and thus, the technology and training centers those within them have. So like, if you develop the crafting skills, or commission a certain kind of training building that brings everyone's level up to 5 or 10 or whatever, or get access to your town for a certain kind of resource, your character would be more well-equipped when you pop into them after an old one dies, but it wouldn't be like you were possessing them with your own level. It seems to me it'd strike a balance between permadeath being too punishing and not punishing enough, as well as tie the game more closely within its theme. Though I'd have to play the game obviously to see if that was true or not