It sounds like they are treating you as an independent contractor and simply paying you a commission. If so you are running your own business and need to pay your federal, state and city income tax just like any other business. The fact that the firm paying you is in the Bahamas really makes no difference; you are in New York, not the Bahamas, and thus pay US taxes.
If you are not an independent contractor but rather an employee, then they are doing business in the US (they have an employee, you, in the US) and they will be subject to US taxes and filing requirements. In this case they will need to comply with all the US requirements on employers such as unemployment insurance, workmen's compensation, FICA and income tax withholding. They will also need to issue a w2 form at the end of the year.