In general, whatever "magic element" used in their world can be replaced by the "magic" that exists in Empatheias (in this case, that would be the natural elements of the world). Another alternative is using emotions as a fuel, or a mixture of both.

Thus in Milla's case, she would be able to use her spirit artes without the need to channel spirits. Instead she would just draw power from the elements (and/or emotions) around her. For her it will feel a bit different, but in practice it would be basically the same. In addition, the Four are allowed to come with her and rather than mana they would just take in the elements and/or emotions around them.