Sponge diving wasn't limited to Kalymnos. There were sponge divers all over the Aegean. After Chernobyl (it is debatable whether it is related) the sponge population crashed and basically killed the industry. Only the divers on Kalymnos hung on.
Being as poor as they were, they'd push the limits to get as many sponges as they could. They also found a lot of shipwrecks, some of which they looted and sold on the black market. This still continues to this day.
My first visit to Kalymnos in 2011, there was this 1 meter high half a meter wide amphora used as decoration at a laundromat. I've seen looted antiquities in homes. In 2015, due to the acceptance of the reality that most homes in Kalymnos had looted antiquities and that Greece doesn't have enough museum space for the antiquities that it has (as told to me of a former senior archaeologist in the Ephorate of Underwater Antiquities), people were required to register their artifacts.
I am skeptical of the hourglass. Some may have used it. The sponge diver I know (a rather controversial one due to his son) never mentioned it. I suspect that it was trial and error that they figured out how long they could stay down. If they couldn't light a cigarette back on board, they knew they were in trouble.