Android :: REST And Listviews Refresh?

In my app, I have different activities with listviews. The datas come from a server with a REST method, and it's only done once, when I start the application.

The pattern that I'd like to set is to precharge all the listviews with the JSONs that I already have in local, and in parallel, launch a thread that get the new JSONs files with my REST methods, and then update the listviews.

For now, when I start the app, I parse my JSONs files, and build all the lists of objects. I access them later in a static way, from my lists adapters.

So I would like to know the best way to launch this REST thread, and update the listview. Should I use AsyncTask ? A service ? and then, when I update my local JSONs, I have to re-parse them, updates the lists of object, and call in my adapters NotifyDataChanged ?