Jetpack uses your WordPress.com account to create a "Jetpack Site" record on our side, which handles stats, the shortlinks, processes Publicized posts, processes incoming Jetpack Comments, handles the index for Related Posts, etc.
With that record, we keep the basic settings (e.g. site title, home and site URLs, etc). Generally and typically, when changing domains, this gets updates as expected on our end. Sometimes it doesn't for a variety of reasons that we have on the roadmap to investigate further and reduce as much as feasible the times this happens.
In your particular case, the overall URL setting was stuck on the IP address, so when using the wp.me shortlink, we convert the link to an association with the post and then, the full URL.
The tl;dr was this isn't supposed to be a problem, we're working on reducing when this problem happens, and if/when you change domains, please do check a shortlink to make sure it works and, if not, drop us a note here or via http://jetpack.me/contact-support/ .