Here's how you can make the TrackingTime Chrome Extension work with a self-hosted version of Jira.
If you haven't already, download the TrackingTime Button extension for browser. It's available in Chrome, Safari, Microsoft Edge and Firefox.
Once installed, please click on the extension button in Chrome's toolbar to login with your TrackingTime account (the email and password you used to signup for TrackingTime)
At the bottom right in the extension, click on the settings button.
In you settings navigate to "Custom Domains" write your domain without the http:// and select jira.com rule and click "add domain".