Different states has different requirements regarding the extension. What you can do (especially if you are using TurboTax Online) is to add NJ and RI also, prepare the extension, and select any options for state extensions. Some states do not require their own extension, they are okay with the Federal extension. You should get advised accordingly.
Technically speaking, yes you will have to report the income derived from each of those states. It is possible that the income in question is not enough to actually be taxed in the state, but it's hard to know that now. If in doubt, file all applicable extensions to avoid any late-filing penalties. If you think you might owe tax, follow the instructions to make any estimated tax payments to avoid any late-payment penalties.
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