Did Bethesda do this because PS3 users got Dawngaurd last? Is that why they released Dawngaurd last, so they could add all these missions that have you interact with NPC's from Dragonborn?

I doubt it. It's just how these quests work, if they can target any person or location in the game, they sometimes target those added by a DLC. It's the same with radiant quests sending you to retrieve an item from cave X - it may be on Solstheim.