You would also remember that under the exchange rate mechanism (ERM), countries were required to intervene in foreign exchange markets to keep their floating currencies within the agreed band. In short, the convergence criteria had “teeth” and carried sanctions.
In the case of the Caribbean, the convergence criteria seem to be purely for information purposes; they have certainly not been seen as a guide to policy; there is no official monitoring; there are no sanctions; and none of the participating countries seem anxious to yield sovereignty over economic policy.