Isn't it actually a 3/8ths hey?  ...Which is somewhat tricky to say: Three Eights Hey For Four.  Lots of numbers in there.  Good enough reason to find another explanation.  ;-)

What I'm seeing about not simply writing it out as a hey is that the star is causing the ladies to move forward into the men's position.  From a static perspective it is definitely a partial hey, but the women's momentum will want to carry them too far forward and it'll become mush for anyone not paying attention.  Turning back to the right is nice flow, and to me there's nothing wrong with writing things like that into the dance.

For example, I have long used a dance which cues the ladies to turn AWAY from a star and swing the man behind them.  Technically it is just a u-turn, but every time I use that phrase three quarters of the ladies will turn TOWARD the star (for a variety of reasons, including partner "assistance").  It makes me cringe, because the dance is so much nicer if they turn the other direction.

Neal