For Dark Knight, Machinist and Astrologian, which started at level 30, you had to have a level 50 job to be able to unlock them. But that was perhaps because you had to have the ARR story completed, and the last story quests were level 50. So you may not have to be level 60 and have completed the Heavensward story to unlock Samurai or Red Mage this time around. In fact, in Frankfurt Fanfest Yoshi P said something about not requiring Expansion area access to unlock these jobs. No mention of required level that I know of, though.

I think it's safe to assume you'll have to be at least level 50 if not 60 to unlock them.