Holy cow!! I just hit the jackpot, it seems! The funny thing is I knew Palermo indexes were coming this year to Ancestry, but my 3-month trial from the software ended in March. Wow, that's funny!
I am amazed by what you've found, and thankful for the time you've taken to find it! I really appreciate this.
I am trying to reconcile differences in "facts". Here I go thinking out loud:
So, my first line of evidence was a photocopy from a marriage record book in a church in New Jersey, which stated Vincenza's marriage to Francesco San Germano (possibly born 1902 to Charles San Germano and Rosa De Carlo - funny enough though, the last name San Germano was translated literally from San to Saint and is written as St. Germano, haha). In this record, it lists both Vincenza and her new husband's places of birth as Casteltermini. How neat they are from the same place as kids - likely the parents knew each other? Anyway that was my clue of where in Sicily to consider. It also listed her Baptismal date and place as June 12, 1908. So I presumed she was born before this date. I then looked at my notes that I had transcribed from my grandmother (Vincenza's daughter) which said she was born June 12, 1906. 2 years to wait for a Baptism in Italy? Seemed unlikely to me. Its no wonder I didn't recognize the Ellis Island record at first, which places her age of 7 in 1916, meaning born in or around 1909. Odd difference in the year of birth (3 years), but the location Casteltemini is the same. It also shows the parents' names (Calogero & Calogera), which match those of the marriage record from NJ. Then we have the record you produced above, which shows a birth of June 12, but 1909 - not 1908 or 1906. So right date, but different year than on the marriage record from NJ or my grandmother's memory - yet it agrees with Ellis Island. It, too, contains Casteltermini and the parents names. So either this is all a huge coincidence with first and last names, OR, more likely, the record in NJ and my grandmother's memory are incorrect. I would guess that's the case. To be sure, my grandmother told me Vincenza's parents names were Charles Scarna and Charlotte (my grandmom's namesake) Scozzaro. Well, Calogero and Calogera seem close enough to Charles and Charlotte by my untrained eye, but maybe someone here can clarify. Just a case of "Americanizing" a name? In any case, I am waiting to hear from my grandmom on confirmaton of Vincenza's siblings names, hoping they match those names from Ellis Island. We will see. My ultimate guess is the information you provided me matches my great-grandmother, but its the American information (NJ record, grandmom's memory) that are mistaken. Hoping that's the case

Wow, I am reeling from this information - and scans of documents, no less! How cool! I didn't expect much of an answer, and so quickly - I am pleasantly surprised and thankful!