I have been wondering about this for some time.  The one thing that stands out most obviously is that since they are not 'exposed' to the One Power in the steddings, that must be the cause for the Longing effects.  Have the Seanchan found a way to block their exposer?  Maybe it is some hybrid form of stilling that cuts them away from the source - though they can't use it, maybe there is some connection that causes them to be effected by it.  Maybe it has some sort of opposite effect it has on humans?  Maybe Loial and his wife would benefit from this and continue Outside?

 

Another theory could be that they found a some Ogier who weren't effected and those went on to reproduce and create a society uneffected.

 

Anyone have any other theories?

There are multiple threads on this already. RJ said that Seanchan ogier never lost the steddings during the breaking b/c there are more, so those ogier never got the Longing.

Excellent reply, Queen JLM.  ;D