So I have been fighting this problem for two days and still, no solution found. I tried with brand new Unreal Engine projects, different IClone models and the newest version of the plugin and non seems to do anything.
The problem is this:
Whenever I Export an animation from IClone using Unreal Engine presets and then import the animation Unreal Engine, the model that plays the animation gets very twisted. I tried to import the animation with the same mesh it played inside IClone but the same problem still remains.
Here are the steps:
I apply animation to the model
67% of original size (was 753x772) - Click to enlarge
I Export as FBX using Unreal Engine presets:

In Unreal Engine I import using default presets:

The animation is distorted.
67% of original size (was 753x772) - Click to enlarge
Strange thing is that when I press import and get the Auto Setup menu and I disable using the auto setup, then the character and animation come normally and work, but as soon as I allow Auto Setup, the twisting happens. I tried to import the character using Auto setup and only animations without it, but that didn't work and twisting happens.
67% of original size (was 753x772) - Click to enlarge
So every help is much appreciated! Oh, and I guess I should mention that I tried to bring Unreal Engine mannequin to CC4, characterized it and put animation to it and that worked. The default CC characters have the problem.