in this case , the eyes are made with DFormer
That mean flat eyes, but are rollable
The Problem you can not export DFormer.
It will change the eyes to spheres again . Therefore it looks like popping out .
For that you need extract the eyes and import it seperatly to iclone.
Then use the Avatar tool to make the eyes movements and then scale the Eyes flat again to fit with the Head
Is not a easy to explain the whole workaround in few words .
But it is not impossible to do.
I had do it for some of my own Character, too.
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liebe Grüße vidi