The Catholic Church is the only organization that can offer “actual” Christian exorcism, so all those exorcists are just random “exorcist-trained” priests living in the Vatican.
In my head canon there's kind of a "flag of convenience" thing going on there. You know how a lot of countries register their ships in Panama or Liberia despite the ships and the companies having nothing to do with those countries? I like to imagine it's the same with exorcists and that a lot of them are just registered in Italy (because Pope and Catholic church HQ and all that) but actually live and "work" in entirely different countries.
Although the idea that Italy just has a couple hundred exorcists running around shouting "La potenza di Cristo ti costringe!" at random people on the street is also somewhat amusing to me...