Hi priyankadave - I've been testing this and I can confirm that I am seeing this same behavior as you are. It looks like this may be a bug in the system that was introduced in the latest version of Jive. I've filed a bug around this, under ID JIVE-55164.
One interesting note is that when I enable the "News" feature, the Inbox indicator that will show even when the inbox is empty. I believe this is also what the expected behavior should be when News is disabled, such as in your instance, which is why I've filed a bug for engineering to review.
In the meantime, the best workaround I can think of would be to edit your theme to add a new custom navigation menu called "Inbox" that would simply link to "/inbox". This would create a new link that would go to the user's inbox, like this:
David Bastedo thanks for the quick response! Have implemented the workaround for now. The users can now directly and easily access their inbox and also create custom streams ( a useful feature for our instance).