Should I be concerned
If you are reading this page, then it is safe to assume being anonymous (less unique), and remaining so is of great interest. Users with a serious intention to research these issues are encouraged to assist in accordance with their skills. Testing, bug reporting or even bug fixing are laudable endeavors. If this process is unfamiliar, understand that about thirty minutes is required per message / identifier to ascertain if the discovered result  is a false positive, regression, known or unknown issue.
To date, none of the various leak testing websites running inside Whonix-Workstation ™ were ever able to discover the real (external), clearnet IP address of a user during tests. This held true even when plugins, Flash Player and/or Java were activated, despite the known fingerprinting risks. Messages such as "Something Went Wrong! Tor is not working in this browser."  (from about:tor) or "Sorry. You are not using Tor." (from check.torproject.org) are in most cases non-issues. If the real, external IP address can be revealed from inside Whonix-Workstation ™, then this would constitute a serious and heretofore unknown issue (otherwise not).
It is unhelpful to ask questions in forums, issue trackers and on various mailing lists with concerns that have already been discussed, or which are known issues / false positives. In all cases, please first search thoroughly for the result that was found. Otherwise, the noise to signal ratio increases and Whonix development is hindered. Users valuing anonymity don't want this, otherwise this would violate the aforementioned assumption.
If something is identified that appears to be a Whonix ™-specific issue, please first read the Whonix Free Support Principle before making a notification.
- From a browser test website, in a log file and so on.