As others have mentioned, it needs cookies permissions:
https://help.rescuetime.com/article/90-the-rescuetime-firefox-add-on-does-not-work-with-my-custom-privacy-cookie-settings-in-firefox

Worked like a charm!

It helps you be productive

Excelente aplicacion que me ayuda a ser conciente en ue uso mi tiempo

After a long time, I can finally confirm it is working on macOS and Firefox with a cookie whitelist (cookies disabled by default, only user-specified pages are allowed to set cookies). Thanks to the developer to create an actual support document for this edge case.

If you are a Firefox user who likes to whitelist cookies instead of accepting everything by default, here is your guide:
http://rescuetime.helpscoutdocs.com/article/90-the-rescuetime-firefox-add-on-does-not-work-with-my-custom-privacy-cookie-settings-in-firefox

Simple, concise, works well, helps me saving time

Since Firefox 57 I've switched over from Chrome. This extension initially did not log correctly even though the notes here said it added support for Firefox 57. However, I recently received an update to my rescuetime OSX app and now everything works perfectly as expected. Thanks rescuetime. This is now a 5 star extension.

Best way to keep track of what you actually get up to on the internet all dang day - warning: may be eye opening.