Adding to the others, there's two of boost/skip.

1) Job boost - This is what you've bought. It has given you a level 70 red mage, and it has also completed all the red mage job quests (level 50-70) for you, but that's it.
2) Story skip - Skips the story to either the start of Heavensward (quests start at 50), Stormblood (quests start at 60) or Shadowbringers (quests start at 70), depending on which one you purchase.

Job quests are separate to story quests.

So what you have got is a level 70 red mage which is capable of doing the story still, you're just drastically over levelled for it is all.