Hi, nice to hear from you. Thank you for answering me.
I have since learned a little bit more about my ancestor, Rafael Fernandez Alvarez. He was my great grandfather. He was born in Asturias, but eventually he ended up in Cuba. He married my great grandmother, whose name was Carmen Cienfuegos Campos.
My grandmother (their daughter)'s name was Carmen Piedad Fernandez Cienfuegos. She was born in Cuba in 1883, so he has to have arrived in Cuba sometime prior to 1883.
There is a tradition in the family that he was in the Spanish military during the colonial phase of Cuba's history, but I have yet to confirm that.
Hopefully some of this fits with your history; if so, you would be the second branch of my family that I have found through genealogy :-)