Originally Posted by
synesthetic
If we're going to quote the OP's linked article..
" “We were actually recently deciding what to call these jobs that don’t have a base class, and we’ve decided to call them ‘Extra Jobs.’ Just like when you can switch to different jobs when you’re at level 30, that applies to these as well. As long as any class or job is at level 30, you’ll be able to access any of these three new jobs.” "
There is no unlock quest.
The Ishgard quests should be for additional skills and story.