Yes, that's exactly how it should work. Same as a Chip and PIN card.
We developed an NFC-based protocol that does pretty much exactly what you've described (uses a POS terminal not an app for security reasons).
Final version to be released in dec. Let me know what you think: The (draft) white paper is available for comment at <!-- w --><a class="postlink" href="http://www.opencxp.org">www.opencxp.org</a><!-- w -->