Dear Vladimir,
Most likely, the issue is that the add-on hasn’t been manually added to the Jira ticket yet. By default, the plugin appears automatically in every issue, but in some cases—depending on user settings—Jira may require you to add it manually at least once.
To do so, simply click the "Apps" button under the ticket title, then select Time Tracking App. It will immediately appear in the issue. You can also click it again to hide it if, for example, you're taking a screenshot or sharing your screen and don’t want the add-on visible.
In any case, the functionality works as expected. It’s always more constructive to reach out to support with a question before assuming something doesn’t work.