Actually, you either have to call clear/add on the adapter, or create and set a new adapter. The adapter does not retain a reference to your list (it is only calling toArray on your list at construction), so there is no way for it to update itself.
dataAdapter = new ArrayAdapter<String>(this, android.R.layout.simple_spinner_item, newStringList);
dataAdapter.setDropDownViewResource(android.R.layout.simple_spinner_dropdown_item);
spinnerCategory.setAdapter(dataAdapter);