I've 'solved' this problem. I'm loading the Twitter Intent (TI) page in the background as soon my index page is loaded.
While the TI page is loaded, it closes again. The page is in cache now, next time TI is loaded everything is instant correctly.
You can find more about background loading here: developer.mozilla.org/en-US/Add-ons/SDK/High-Level_APIs/tabs
In this fiddle is shown how I did the trick; FIDDLE