You must republish the application to OpenShift Online in order to see the home.html changes reflected in your default system web browser, as detailed here.

To republish the application, in the Servers view, right-click the ticketmonster at OpenShift server adapter and click Publish. At the prompt asking if you want to commit the project changes and push them to the OpenShift Online Git repository of the application during publishing, in the Git Commit Message text field type Updated home.html and click Yes. Once the application is rebuilt and redeployed, the Console view displays the following:

Deployment completed with status: success

To view the changed application in your default system web browser, click the Reload icon. Alternatively, in the OpenShift Explorer view, expand the connection and domain. Right-click ticketmonster and click Show in Web Browser. The text is updated to reflect the changes made to home.html, indicating that you are viewing the updated running version of the application.