Currently it’s all saved locally but the devs have just announced 0.9.0 which is when they let everybody else on to MP, there isn’t a date for it yet but it’s unlikely to be before September. When MP is launched then the MP side of things will be server-authoritative (the server checks what your client is telling it & the server trusts itself over the client if there’s any difference of “opinion”) & the MP saves will be on their servers but the Offline characters will remain saved on your pc.