Being the world's leading producer of bauxite, globalization has increased Jamaica's consumer base and international relations. And given that two of Jamaica's largest sources of income are tourism and remittances, (namely the latter), any international relationships which may potentially lead to business opportunities have likely been aided by globalization. In theory, globalization would help Jamaica become more integral in world markets (notably, sugarcane, bananas, and their major resource, bauxite).
However, Jamaica is still a post-colonial country, having been under control of Spain then England for 4 centuries. Gaining independence in 1962, no longer with the support of their colonial economic superpower, England, Jamaica was free but now a "developing country" economically speaking - Under a socialist democracy but gearing towards a more free, open market by the 1980s. Around this time, largely under the influence of the US and UK, the World Bank/IMF was trying to remake the world as a global free market, which included loaning money to developing countries. Jamaica received a loan from the IMF, but it had ridiculous strings attached, including forcing Jamaica to remove import taxes on goods and market interest rates on the loan itself, with penalties for being late.
The IMF, in this respect (and there are examples with other developing countries), behaved the way credit card companies and mortgage brokers behaved/are behaving in regards to the housing crisis. I.e., loaning money, knowing the borrower probably won't be able to repay: with consequences. With Jamaica, however, it was the sanctions and nearly imperialistic strings attached to the loan which put them so far behind.
This, coupled with the fact that, by opening up its market, say in the case of bananas, the local Jamaican banana producers cannot compete with the United States, so they drop their prices, and logically following make less money, and in the international market, they fall behind. Also, labor is outsourced to Jamaica by clothing stores like Ralph Lauren where local Jamaicans work for much less.
All that being said, globalization does open opportunities for developing countries, but it also opens opportunities for those countries to be exploited for their labor, resources, and interest payments. This may sound one-sided, but I would say that the benefits of globalization could benefit Jamaica as long as the IMF removed its sanctions and as long as Jamaica retains the right to regulate its imports and exports: not to mention, the ability to regulate wages of their own laborers working for foreign companies (I.e., natives working in Kingston working for a US clothing company should be making more than 5$ a day).
Check out "Life and Debt." Documentary about all this.