Raids are side stories at 50, 60, and 70. You won't see any just sticking to the main scenario quest.Are there no raids until lvl 70? It has just been dungeons and trials so far, also any story progression tied to them?
The raid for lv 50 is tied to the calamity/Bahamut seen in the intro movie. The raid at 70 is tied to the events directly preceding Stormblood. All the other raids have their own self contained stories iirc.