My grandmother's second last name is also Rufin, her mother (my great-grandmother) was Sofia Rufin Aguero, Rufin spelled with only one "r". The story I was told by my grandmother about that side of the family is that Sofia's father originated from France and emigrated to Cuba via a boat from the Canary islands sometime in the 1800's. I am not sure how many siblings Sofia had, or whether her father was born in France or in the Canary islands to French parents. But I know that Sofia was born in Cuba to a Cuban mother. My grandmother had two faded photos of her, she had large light-colored eyes and long, black hair with cork-screw curls. I have many questions regarding that side of my family as well. I am from the Rufins of Matanzas too.
I do know that the Rufin family is not always the same as the Ruffin family. I've been trying to find ship registry records from the Canary islands of the Rufin family to no avail.