No. No, no, no, no. A lot of terrible things were done to people who opposed the government, but mass killings like that are not the norm. There are lots of propagandist websites that claim everything under the sun, but if you try to actually verify their claims you'll find that they can't actually prove even a quarter of what they claim.

The period for which firing squads were a normal occurrence was a brief span at the beginning of the Revolution when the government was trying to push through some summary justice on former members and supporters of the Batista government (which had tortured and murdered many Cuban civilians). The firing squads used, after quick political trials, were tools in order to a) keep people from taking justice into their own hands, like they had after the Revolution of 1933, and b) get as much quick and cheap popular support as possible (executing the murderers, corrupt officials, and torturers of the Batista regime was easily within their power and fostered support and legitimacy among the populace).

After that, while firing squads have been used, it has been more sparingly. You basically had to commit very serious crimes to be even considered for a firing squad. Even Comandante Huber Matos, who was given a quick political trial in the early 1960s (after the firing squads had largely ended) was simply sentenced to an extended prison sentence for opposing the government's turn to Communism (he has since been freed and died only last yera, while in exile). Firing squads were used in more recent cases, like in the case of General Ochoa who was found guilty of drug trafficking (c. 1989). The most recent case (though we are getting into recent history) is the 2003 hijacking of a small boat, during which the criminals threatened to murder all the passengers unless their demands were met (they were allowed to leave and given enough fuel/supplies to do so). Hijackings and murders related to these had gone up, so the government used Capital Punishment to make an example of those hijackers.

I have not even heard of a single case of a defector's family having been 'shot' because the family member defected. While I'm sure that someone, somewhere, may claim it, in all my time there and study of the island I have come across 0 evidence for it.

Family members of those who defected could potentially have no repercussions at all. One of the most outspoken anti-Communist intellectuals/critics of the Cuban government is Rafael Rojas (currently living in Mexico). His brother, Fernando Rojas, is currently a Vice-Culture Minister. No jail time. Nothing.

What used to happen to Cubans who left (and to their families when said families were suspected of harboring anti-government sympathies) were 'actos de repudio' or 'acts of repudiation'. These were government sanctioned, and often enough government organized, political rallies in front of the houses of defectors. Pro-government music, like Silvio Rodriguez, would be played, rotten eggs would be thrown (less common now that eggs are so expensive but very common in 1980s Mariel Boatlift era), and insults shouted (escoria - trash, gusano - worm, etc.). An acto de repudio could get out of hand and some punching, shoving, spitting could occur, but they weren't summarily shot.

There were especially strict policies opposing the return of athletes and doctors until recently, but aside from side-eyeing, a possible hit to your career (if you were suspected of harboring political opinions contrary to the government), they were not the victims of the dreaded paredón (firing squad). The government viewed/views athletes and medical professionals as investments (their training especially). Because the US has a long standing brain/sports drain of Cuban athletes and medical professionals. Leaving was, to the Cuban government, breaking the unspoken contract implied by the heavy investment in training them as well as a political betrayal, in that they were bringing the products of heavy Cuban government investment to the employ of the American government.

Op-Ed in the NYT about the brain drain: http://www.nytimes.com/2014/11/17/opinion/a-cuban-brain-drain-courtesy-of-us.html?_r=0

Article on the State Department's Cuban Medical Professional Parole program: http://www.jstor.org/stable/41946012?seq=1#page_scan_tab_contents

Here is an article from the NYT in the late 1990s, including interviews with the families of athlete defectors. No firing squad, no jail time, no being disappeared off the face of the Earth. Alive and kicking, and even giving interviews to the media. http://www.nytimes.com/1999/04/25/sports/what-price-glory-a-special-report-cuban-players-defect-but-often-with-a-cost.html?pagewanted=all

Here is a 2009 NYT article interviewing doctors about their experiences defecting. No mention of families being jailed or shot. No talk of reprisals. http://www.nytimes.com/2009/08/04/health/04cuba.html

Foreign & Commonwealth Office report of the government of the UK from 2012 which also attests to the fact that no capital punishment has taken place since 2003. https://books.google.com/books?id=japuaKWXIokC&pg=PA154&lpg=PA154&dq=capital+punishment+cuba+un&source=bl&ots=kMa6EA9oXB&sig=7S38HEBCQTXoYVg3pS_KKjLVKdM&hl=en&sa=X&ved=0ahUKEwi7gKy08uDJAhWI4D4KHdy7Cus4ChDoAQghMAE#v=onepage&q=capital%20punishment%20cuba%20un&f=false

Moderates have recently gained enough traction that they have been able to override the staunch opposition of Fidel era absolutists. Part of the problem is that much like Soviet Russia the divisions and debates within the party are rarely touched in public.