This has to do with the Free trial. You don't need a product key to install and use a free trial. Normally you would have a license per user, which would allow you to install one copy of Tableau Desktop on your main computer and another copy on a laptop or other secondary device. But if there never was a license or key in the first place that is a different story.
It is a little confusing when you first say, " ...we have successfully activated the license through Citrix machine via Google chrome", but then in the next sentence mention, "...displays to register free trial or requesting an activation key again. I have net heard that one browser opposed to another should make a difference.
I cannot understand whether or not you have installed a paid for license to Tableau Desktop or a trial version. Please come back with more information and I will try to help.