Mr. Fujimori has a normal tourist visa and any resolution is up to the courts. There is a note from the (Peruvian) embassy that is being turned over to Chilean courts, and they are the ones who must decide what happens to Mr. Fujimori.
He can only be arrested if a legal warrant exists, and such a warrant can only be issued by a court that is requested to do so. That request is being made now by the foreign ministry, based on the note from Peru.