Alberti was indicted in July 1963 with 53 other mafiosi after the Ciaculli massacre, which turned the First Mafia War into a war against the Mafia.
In December 1969 he was again in Palermo (while he was supposed to be in exile) when Mafia boss Michele Cavataio was killed by a Mafia hit squad for his double-crossing role in the First Mafia War.