Column specific term sets that you create will by default be assigned to the site-collection hosting the site content type gallery in which you create the site column. Such term sets will not be visible in the Term Store Management Tool in Central Admin, even if the MMS connection is set as the default storage location for column specific term sets. This also applies to column specific term sets created in the content type hub.
Do not create column specific term sets in a content type hub, this will break the content type publishing. If you click "Manage publishing for this content type" you will get this error:
The current content type contains a managed metadata column that uses a customized term set that is not available outside the current site collection. Please change the column setting or remove the column and publish the content type again.There is, however, a third option in addition to the two suggestions; moving the term set from the site collection term group to a shared term set group in the managed metadata service term store.
Move the term set, then verify that the content type publishing setting is Republish in the content type hub. In Central Admin, run the "Content Type Hub" job first, then all applicable "Content Type Subscriber" jobs to execute the actual publish-subscribe process. Finally, open the site content types inventory in a subscriber site-collection and verify the subscribed content type, site column and term set.
I also recommend updating the site column definition to use the "use a managed term set" setting after moving the term set into the core term store.