Evelyn was originally feminine - it's a matronymic surname, a medieval form of
Aveline. Eventually it only survived as a surname, and family surnames were traditionally given to boys as given names. The same thing happens with names such as
Avery,
Emmett,
Wyatt,
Winston,
Eliot - old English names that only survived as surnames, and then became given names again thanks to the practice in English-speaking countries of using surnames as given names.
Very often, the names "switched gender" because people are unaware of its etymological origins (such as
Emmett being a nickname for
Emma, or
Evelyn being the same as
Aveline).
As for the pronunciation - it seems to me that Eve-lyn is the traditionall pronunciation, and Ev-a-lyn may be inspired by the names
Eveline and
Evelina.
Alexandrina, Annabella, Clementine, Charlotte, Emilienne, Florence, Frederica, Katharina, Mary (May), Maud, Penelope, Rosamund, Theodora (Teddy).
Aubrey, Axel, Benedict, Bertrand (Bertie), Cuthbert, Dashiell, Everard, John (Jack) Leopold (Leo), Magnus, Matthias, Maximilian (Max), Wilfred.