There's some confusion between the Travel Authorization Form and the Immigration Form in this thread.
The Travel Authorization Form is no longer required so we'll stop discussing that here.

The Immigration Form that has always been required and is normally filled out during your flight to Jamaica, can now be filled out online in advance....but....
the problem with filling out the Immigration Form online happens when you get up to the Jamaican Immigration Officers and they don't recognize that you've filled out the Form online.
Until Immigration in Jamaica gets everything 'fully' online...it's still best to fill in the paper form while you're on the plane coming into Jamaica.