Puerto Rico has its own Department of the Treasury, aka Hacienda. This is the agency that develops the tax returns (like the IRS does in the US), according to local and federal laws. Every person with employment income etc. derived from sources in Puerto Rico must pay income tax to Hacienda.
Yes, there are incentives for certain new businesses, people with passive income only who move to Puerto Rico, existing businesses that fit into certain categories, etc.
To say that nobody who lives in Puerto Rico pays taxes is not true.
For somebody who only lives on passive income you should check out Law 22. If you reside in Puerto Rico for at least 183 days out of every year, you pay no taxes on the passive income. See prinvestmentsummit.com/laws