The point to note is that this visitation record states that the earliest Neville was a Gilbert who was admiral in the Conquest of England in 1066. Absolutely no evidence can be found to support this save that his descendants, around 1150 or so when coats of arms were invented, used arms whose principal charge was a ship.
The best account on the early Nevilles is by Ethel Stokes in Complete Peerage Volume 9, pp. 502a-d; she did this from the surviving documents of those times. It is her account that is followed in my main database.