hi cbessonleaud, theme panel additional css is not mean to added with child themes. it also not added within parent css, but it will print on header of your HTML file. i don’t know how you can conclude our additional css section will copy the text within child themes.
if you need to add css on child themes, you will just need to alter style.css file in child themes.
I thought that the Theme Options were saved in the child theme to avoid being erased by parent theme updates.
Therefore I concluded (too quickly) that the additionnal css section add css to the child theme.