Regarding the evil spirits thing ... and coming at it only from the pov of a manga reader, we have seen that magic does indeed exist in the world (of course) and does have a direct effect on things, and we have been informed that "demons" (whatever those are - we have not outright met one yet) exist too.
At the same time we have Falma's giving of compounded medicines to lessen the effects of the mental disorder of the lady in this chapter. But there was one thing he mentioned, and that was "I don't know what caused it". Such triggers and resultant states can be caused by any number of things - physical trauma or biological change or heredity or some sort of element outside of one (like eating something we react to really badly or being exposed to something that totally throws off the natural balance a person previously had, etc.) ... even nowadays there are cases where a trigger is not always apparent nor easy to discover.
Nonetheless the response Falma gives of the cause of many of the subjects for exorcism being able to be healed through medicine is "probably" (I assume the source material uses the same or a similar word) - which I read as him coming from the vantage point of the body of knowledge he is most familiar with in the world he inhabited for many years before this one.
Setting aside the possibility of an outright possession (which has not been directly disproved in this fantasy setting thus far) perhaps these "demons" could also be a trigger of some sort with some sort of magic for causing these sorts of effects in individuals? In other words there are all sorts of things that could be which have not been spelled out yet but which would not be hard to build from even the snippets we have been shown of the world and its inhabitants thus far.
Falma is continuously finding out new things about the world he inhabits now (like his growing awareness of his abilities, for example), and it has some similar things but some dissimilar things as well to his previous one. So yes - it seems possible to me that events might occur later on that would force him to amend his initial assessment of saying that exorcisms could largely be healed through medicine.
Wow ... that was a lot longer than I expected! XD