Brass is made by a series of draws. As in the brass starts out as a cup and is gradually drawn out to its cylindrical shape. That process makes thicknesses uneven. It's just the nature of the beast. Because if this, if you use a bushing die without turning the necks, you're pushing those inconsistent thicknesses to the inside diameter of the neck. That results in an inconsistent amount of tension on the bullet which equals inconsistent pressure and velocity.
A mandrel pushes those inconsistencies to the outside diameter and leaves a uniform amount of tension on the bullet. No neck turning really required.
An expander ball/button is inferior to a mandrel because it pulls and stretches the neck and shoulder back out as it exits the case. Mandrels size in a downward motion and do not stretch the neck or shoulder as they exit the case.
As we all know, the neck of the case opens up when firing. You want the neck to release the bullet evenly and consistently from one round to the next. That's why it matters having the inside wall of the neck uniform.
Once the round fires, the pressure pushes the case into the chamber walls, and pushing any inconsistencies in thickness back to the inside of the case. At that point it really doesn't matter though because you'll have to resize everything again anyways.
If you turned the necks, you don't need to do it again. If you didn't, like I said, the chamber will have pushed those uneven thicknesses back to the inside of the neck. That technically doesn't matter though, because FL sizing without an expander ball will do the same thing. The mandrel is what fixes that.
It is good practice to anneal though. A mandrel can't defeat spring-back of the metal as it work hardens. Once work hardened, those inconsistent thicknesses will spring back and tension will once again be uneven. Annealing will undo the work hardening and allow the mandrel to set uniform tension once again.
If you turn your necks, a bushing can do the same thing a mandrel does. Turning your necks is what ensures the necks are even thickness and makes it so there's not more pressure on the bullet from thicker areas of brass.