While I agree with you that Gina was undoubtedly presented as being of Hispanic/ Cuban origin (mainly because of her apparently fluent Spanish to my perception), and I recognized that Calabrese was an Italian-origin name, I also agree that the story of her mother Elena Obregon was tacked on with no prior reference. In fact, Gina told Sean Carroon that she had several brothers and sisters (without saying if they were older or younger, or really giving any info about her family). There was never any explanation of, or reference to, her ancestry/ heritage--just as all of the others were barely hinted at.
Tubbs' brother was killed by the Calderone gang, Crockett was a football star at U of Florida and served in Vietnam; when the show starts his marriage is on the rocks and he has a 6-year-old son; Switek is an Elvis fan, Zito is from Staten Island, Trudy has an old boyfriend, Castillo did some top-secret work in SE Asia for "the agency" and had a Chinese wife who he thought was killed, but wasn't. He was also ambushed, attacked and left for dead--seemingly by men on his own team. When he recovered he left the agency and went into police work to continue to fight the drug traffic. The lack of background and detail made it easier for the show runners to add in details later that don't necessarily relate to past history, but also might have happened.
For me, this family history for Gina made sense and was something that could have happened; however, I can see why some think it was a "mistake" or "debatable." I do think a lot of people seem to feel this was tacked on, and not necessarily gracefully.
Virtually everyone's background was very lightly sketched. Castillo had the most background--but EJO was given control over his character to a degree that none of the other actors were. For me, Season 3 is not too late to add depth to a character's canon identity. The way I reconciled this story into canon was that after Gina's mother was killed, she was given to her aunt (mom's sister), who may or may not have been married. If she was married, her husband could have been killed during the revolution when Castro came to power. Aunt then refugeed to Miami with Gina and any other children she may have already had. In Miami she met Mr. Calabrese and married him. They may have had more children together and continued to raise Gina as their own daughter. Aunt may not have told Gina about her birth mother's story until Gina was an adult.