Leaving and taking our business elsewhere is exactly what I have done....and yes, the proprietor knew I needed ( not wanted, NEEDED) to have a smoke free experience.
At a well known, upscale steak place in Maho, a table smoked cigars next to us. Not only did it interfere with tasting and enjoying our food, wine, etc...but it nearly landed me in the hospital needing a nebulizer.
I've even had issues on the beach at Karakters, when 3 pack smokers aimed it right at me.
Unfortunately, it's I who must run for upwind locations or leave.

As Pat said, we cannot expect the same health issue enlightenment, and awareness of the second hand nature, and dangers of smoking in another country. Behavior in SXM in regard to many things seems to be that people feel freedom to behave as they wouldn't otherwise.