Based on something I read in the response presented in this question (https://dinonline.org/2015/11/07/hachana-by-non-jew/) I have a question regarding a maid doing the dishes on Shabbos (either for later use on Shabbos or because of discomfort about having dirty dishes). I always heard that since it is mutar to wash the dishes on Shabbos we don’t have to worry about it if she chooses to use hot water for her own benefit. My question is regarding what I learned about a non-Jew doing malacha for a Jew in a Jew’s domain when it is adaitei d’nafshei. They can only do the melacha when it is not in the Jew’s house. Why is doing dishes with hot water in the Jew’s house different? I was thinking the reason is because everybody knows that she is washing the dishes in this fashion for her own benefit and nobody will be chosed the baal habayis as having made her a shliach to do the melacha. Please let me know the mechanics of how this works. Thanks.
Your explanation is the correct one. Any activity which it is clear to all that it is being done for the non Jew’s personal benefit, and it is something insignificant that she would not need to ask permission to use, but can do so on her own, poses no problem.