The quest level immediately goes up to Lv80 once you complete that quest.

I think it's done that way because you can get to that point where you're told you'll need to complete your Lv80 job quest while you're still Lv79. Otherwise you might find yourself blocked by quest level, go away to level up, come back to pick up the MSQ again, and almost immediately be told that you can't progress because you should have done your role quest!