If the "Popular Music" part of Twitter Music is empty, it is because your country is not supported. Here is how to fix it.
The JS calls "https://music.twitter.com/app/chart/popular/*country code*/rdio/" via ajax and returns "404 NOT FOUND", it doesn't understand your country code.
But you can fix this by overriding the javascript that handles the country codes. Type this into your Developer console or type it into an userscript:
TM.PLAYER.PLAYER.getCountryCode = function(){return 'us'}