In this day and age I would think that they would want to promote the fact that they are a smoke free resort. That would be a draw (no pun intended) for many travelers looking at their options.
I am not a tobacco user but am not offended by those who are as long as they are courteous about it. I have been known to occasionally disregard the prohibition on herb both here and in Jamaica, but always with that same courtesy and a large dose of discretion.
Funny story. One early early morning years ago I was outside my room in the courtyard of one of my favorite beach resorts enjoying a pre dawn spliff when I noticed a Red Stripe (policeman) patrolling the property. I decided perhaps I should take it inside. Later I was telling this story to my friend the security guard and he was very concerned. "He didn't bother you or make you feel uncomfortable did he? Because if they bother the guests we won't let them come here anymore."
Bless...
Ed
