The only plausible explanation which the film provides is that once he murdered Don Ciccio that Don Tommassino inducted him (of course, that assumes that Tommassino was already Mafioso).
Which is what I believe. I think Tommasino was already a man of honor in Don Ciccio's (or Don Francesco's) Mafia clan, and Vito provided him the opportunity to take over this clan and make way for the younger generation. Tommasino, as the new capo of the Corleone clan, formally inducted Vito into the Mafia so that he could become a legitimate Mafia leader in New York.
