A previous post covers the WT popularity and the growth in Cuba:
wfacts
Your point about the growth is an interesting one. The conditions today are quite different from the past, the WT has plenty of freedom to conduct their business under strict official supervision; a lot different that the harsh past persecution.
However the growth has been constant, before the Castro takeover there were about 11,000 publishers with a rate of increase of about 10% annually, about 1994 when the WT had the negotiations with the government that number was 77,000. That shows a steady increase, even with the huge migration out of the country.
I know that in the early years, there was a void in the country as far as religion, culture, social activities and many other things and that many people came to the witnesses looking for refuge and comfort. Many prominent people in Cuban society became witnesses, included were former politicians, military, wealthy people, actors, commercial pilots, professionals and a vast array of “lost” individuals. But it seems that the religion is somehow attractive to the masses, your graphic shows close to a 96,000 presently.
From what I hear from my family, today the JWs work is something different to common life and like a form of occupying your time.
Regards