Leveling a second class - lack of quests?

Ok, here's the situation:

I just reached level 30 on my Conjurer and now level up Arcanist to 15 for White Mage, however I did notice something odd.
There's barely any quests outside of Limsa Limonsa that I can do. Definitely far far less than I had outside Gridonia when doing Conjurer.
I've done both Zones, through Tempest and Zephyr gate, I'm level 8 now and there's absolutely nothing anymore. Total I probably did 4 or 5 quests. That's it.

I had actually looked forward to seeing some of the story for Limsa classes, not the main-Story quest of course, but at least the general quests of the area that are not the main quest. But I'm barely getting anything, I killed a few Dodos and such but it seemed completely random.

Or is that just my wrong impression and Limsa is actually really barren when it comes to newbie quests? I kinda doubt it.
Or are a lot of them tied to the main questline, and since I never did the Limsa Story, I simply can't unlock most of them?

While I don't see it being a huge problem with the first 2-3 classes that you try, I see it being a huge problem once you're on class #5-6.

Mobs,Fates,Dungeons.

I was able to level my CONJ to 15 with relatively little issues, when I was leveling my second class required for Paladin. You only start running into problems if you want to level a second class past level 15. By then, your main quest is sending you all around Eorzea doing quests. While not required, you are encouraged to do every quest in that zone it sends you in.

So it leaves little for you to pick up later. But not really until after 15.