My mother's maiden name is Munguia and I can tell you the few things I know about the Munguias in my family. At this present time most of us live in Texas and California. My grandfather was born in California but before that my great grandparents were born and lived in Mexico. The generation before that came (I as far as I know -and you will find from any history book- originated from)Basque Country. It is a territory between the north of Spain and the south of France. There is a town there called Mungia named after our ancestors (this might be the island that you are speaking about). Mung"u"ia is just the Spanish translation of Mungia. If you google Basque Country you will find out much more about it! There are also some good youtube videos about it.
I do know that it is likely that the family left Basque because of struggles with France and Spain over communism etc.