That is quite *normal* behavior (in any CC version). Hair is trying to conform to a new head shape morphs and gets screwed up in a way.
While there are many ways to deal with it (edit mesh, edit weights, scaling, subdividing, conforming) and probably each particular case depending on a *scale* of damage would require different approach, one would always work fine.
And that is the method offered by Scyra:
Converting to accessory on the base figure which the hair was brought into CC with (selecting a bake option at the prompt).
And then applying it to any other figure, scaling/tweaking transform if necessary and then Transferring Weight as Hair.

UPDATE: I've tried importing hairs with base figures. It helps (thanks Kelleytoons), but some minor problem still exist:

If you compare with image in first message, it seems significantly better, but deffects still exist. If you are going to show this character from 1 m or further away, it will look great, but from 30 cm it does not. 
I think in it's current state it is useless to create hairs content library - better import them when needed, with characters that will wear them. May be Reallusion fixes it in next releases.
Anyway, problem is solved, I know workaround how I can have great looking charater.
Thanks all.