I definitely think it’s worth it to focus on the word choice here, as you do. “Stranger” is such a powerful word (and it lies at the heart of most science fiction). The roots of the word are telling; it comes from the Latin word extraneus, meaning external or from the outside. Jim is certainly from the outside of Julia’s world, and when the boundaries of that world shift dramatically (temporally), it looks as though Jim will be allowed to enter it.