The cause of this issue
Overall, the cause of this issue is poor multi-threading programming. What is happening is there is likely a static method that is being shared that tracks the user's account. If 2 users access a page at the same time, it is using the second user's log-in in the static method and returning for the first user the 2nd user's information.
Testing this issue
Sadly, this is one of those difficult to test scenarios. A load tester will be beneficial but will not be the key to detecting this. The load testing options will simply put the requests you need into the service. I would personally suggest, if you have the skillset, a custom built HTTP requester that will severely thread out about 100 concurrent users. This will not determine your problem but give you the ability to discover the issue.
The next step would be to send request manually through your browser with a different log-in. After a while you should be able to detect the issue and manually verify.
Sadly being what could be considered an intermittent issue this could be difficult to verify. Your best option would likely be to drastically limit the RAM available to your server (I gave Apache since Java but a google search will net results for most other servers). This would slow down the process enough to hopefully detect the problem and be rather repeatable.
Another option would be using debug mode and pausing the execution of the first request and sending a second request.
This means that your developer(s) might not be overly experienced with managing threads. This can be an extremely complex and difficult task. I would heavily test and focus on any and all other multi-threaded portions of your code in order to ensure that they are not experiencing the same issues.