The length of residency for the rental contract may depend on the particular Italian Consulate processing the visa application. I needed a one year rental contract (it did not need to be registered) a few year ago. When I arrived in Italy , I applied for and received a 2 yr PDS. I obtained my visa at the Philadelphia Consulate. Maybe some on the forum can weigh in on the practices of particular Italian Consulates recently.
Umbertomar, I do think things have changed. I know quite a few people who had to have the lease registered. One was definitely in Philly. And lucky you! getting 2 years PdS. We only can get one at a time. Just goes to show it is hard to give advice on this forum because it differs in all regions and at all consulates!