America helps them with many advances in their daily needs. Housing and there government are a few of the things that help Jamaica in what they need help with. Without the help of America Jamaica would not be as civilized and convenient of a country as it already is right now.
To deem Jamaica's culture as too heavily influenced by North American culture is an example of ethnocentrism, in this case believing everything to be about North America. In truth all cultures influence each other in different ways, this does not mean that cultures adopt exact portions of another culture. They often adapt it, and thus it becomes part of their culture more than anything else.
While Jamaica may had adopted some customs of North America, they are still very much their own culture with their own way of living day to day life. And although they may have adapted to some of our routines, we have picked up some of their cultural habits as well and it's usually for the better.