I shoud start another activity only after downloading all information => Make changes as below:
1) Only execute your AsyncTask on button click
new DownloadXmlTask(this, HomeScreenActivity.this).execute("URL");
2) Start Activity inside onPostExecute() method of your AsyncTask:
Intent intent = new Intent(HomeScreenActivity.this, TopArtistsScreen.class);
intent.putExtra("username", username);
startActivity(intent);