I'm not sure I understand what you're talking about here. Do you mean when people shout "inv please" suddenly in a zone, then sometimes pull times are called, and then people scream at each other for early pulling, and why couldn't they have waited, and omg now I'm going to throw a fit for the next few hours?

Those are people talking about Hunt monsters. Each zone has 3 that can spawn, and for the big ones (S and A ranks), people form groups to hunt them. In order the get the maximum rewards, your party has to draw a specific amount of aggro from the Hunt mark. Everyone's aggro in the party gets added together to see what rewards you all get, so you are at a massive disadvantage if you are not in a party.

FATEs work similarly, except the threshold is much, much lower for getting full credit. So, while Hunt monsters are nearly impossible to get full credit on if you're not in a party (especially S ranks), FATEs can be soloed pretty easily.

Being in an FC or not has nothing to do with either of these.