I don't think it's true to say there is no tsunami warning system. When there is a hurricane alert, all local phones get a text message from the CoE about it, I remember having received these. And didn't they test some sort of alarm a couple of years ago which made everyone's phone ping? I'm sure I remember something like that happening. Certainly text messages for sure I have definitely received these.
In any case, I think Dominicans are generally pretty well informed about things like this. Whenever something happens, everyone I know seems to know about it, news seems to spread fast via the social networks and everyone seems glued to their phones most of the time.