The Cuffaro family are Mafia rivals of the Sinagra family, and Montalbano is trying to prevent the outbreak of a full-on Mafia war between them.
The characters are inconsistent in how they pronounce the name of the Cuffaro family.
Mostly it is pronounced as "Cùffaro" (stress on the first syllable) but in some scenes it is pronounced "Cuffàro" (stress on the second syllable).
Montalbano, Fazio and Don Balduccio Sinagra all variously use one pronunciation, then the other. All the others use only Cùffaro, except Galluzzo, who only says the name once, and this is as "Cuffàro".