I have seen this issue before. If you are logged in as root and go to a clients cPanel it
AFAIK logs you in as that user and the root password. So then clicking on the WHM icon could cause some strange results, one reason is probably because you have another WHM open logged in as root (Probably set a cookie).
If you were logged in cPanel as the user then clicked on the WHM icon I am sure it would work fine. When the password box opens I am fairly sure you could put in the users name and the root password and be taken to their WHM.