Two Histories: Sicily in 1493, Calabria and Puglia from 1290
Southern Italy is usually discussed as a unit. For this question it must be split.
Sicily was an Aragonese possession and the expulsion edict of 31 March 1492 applied to it directly. The Sicilian viceroy and much of the island's nobility resisted cause the economic damage was obvious and won a series of postponements. The deadline finally fell on 12 January 1493. Estimates of the Jewish population range from roughly 30,000 to 40,000, distributed across more than fifty towns. In Palermo alone the community numbered around five thousand. Those who could not or would not leave were baptized. Fewer than two hundred converso families remained in Palermo afterward.
The mainland (Calabria, Puglia, Basilicata, Campania) belonged to the Kingdom of Naples, which wasn't Spanish in 1492. Its conversion history is older and messier.
In the 1290s, Charles II of Anjou ordered the forced baptism of the kingdom's Jews. Synagogues became churches. This is the origin of the mainland neofiti two centuries before Ferdinand and Isabella. In the 1380s, Trani's remaining three hundred and ten Jews were forcibly converted and all four of the town's synagogues confiscated. In 1492 and 1493 the kingdom briefly became a refuge for Spanish and Sicilian exiles. In 1495 the French invasion brought pogroms and another wave of conversions. In 1510, with Spain now in control, the Jews were expelled from the entire kingdom. About two hundred wealthy families bought the right to stay. In 1515 the neofiti themselves were ordered out. In 1541 the expulsion became final, and open Jewish life in southern Italy ended for three centuries.
The practical consequence for research: if your family is Sicilian, the decisive year is 1493, and the surviving record is thin but concentrated. If your family is Calabrian or Apulian, the family may have been Catholic on paper since the 1290s and the trail runs through five separate crises, not one.