Never fetch data from an Activity because it will block the UI.
You should extend AsyncTask with parameters and return type as you wish. Do your work on the method doInBackground (@Override it) and on the method onPostExecute (@Override it), call some public method on your Activity to give to it the data you fetched.
Finally, the Activity with the fresh data should feed it to do Adapter.
This is how I always get my data and I get the results 100% as I want (add a progressBar and make it visible before fetching the data and make it invisible after you give it to the adapter).
Hope I was clear enough to you. If you want some code as an example, please ask.
Workflow:
1 - Activity -> new MyAsyncTask(...).execute(); //get the data @Override doInBackGround
2 - MyAsyncTask.onPostExecute() {myActivity.giveFreshData(...)} //deliver the data
3 - Activity.giveFreshData(...) {MyListAdapter.giveMyData(...)}
Altough it isn't MVC this is how you should separate the UI from the data consumption and the data representation.