Fixed it. Basically I reset the adapter, setting the new cursor as the main content. I tried that before, but it didnt work, because I didnt make searchView as global (in class). After making it global, I could use searchView and set new adapter, making it work. In other words:
mSuggestionsAdapter = new SuggestionsAdapter(getSupportActionBar()
.getThemedContext(), tempCur);
searchView.setSuggestionsAdapter(mSuggestionsAdapter);