Your understanding of how passenger oxygen systems work is wrong. The masks work similar to nasal tube systems. They simply add a small amount of oxygen to ambient air. They provide no protection in a smoke event and for that reason both Boeing and Airbus caution pilots not to deploy the system in the event of smoke in the cabin. The oxygen canisters also burn very hot and can generate a light smoke adding to confusion.
In this case the pilots did not deploy the masks. The flight attendants deployed them manually in the cabin. This suggests that Jet Blue's flight attendant training is lacking.