The Italian rules are on Cranio Creations' site. They say:
Territori conquistati: 1/4/10/20 Punti Vittoria per 3/4/5/6 carte carte territorio sulla propria plancia giocatore.
So it's the same as the English as far as I can see - I do not know Italian but this is pretty simple and I see no way to translate it to make the score cumulative.
Also note that in the example picture (which is the same in the English and Italian rules) that the 4 is highlighted. If the scoring were cumulative the example would score 5 so both the 1 and 4 should be highlighted.