In answer to your post, yes the Davila surname is from Spain, from the city of Avila. There are large branches of the name not only in Puerto Rico but also in Mexico and Venezuela. Also in the states of California and TEXAS. In Avila Spain there is a castle that houses a small museum of the history of the surname. Many Davilas were of high ranking at the time of the discovery of America, one of them had the rank of Admiral of the Spanish navy.
I don't think is sephardic, but is possible. There are a few variants of the name, like Davilla, DeAvila, and the French version which is D'avila. Also the Avila surname may be related to the Davilas.