Ho-Oh's Phoenix Turn & Shiftry Ex's Dark Eyes

[pokeMATHter]

My opponent has Ho-Oh from SW active, and I have a Shiftry EX on my bench. If I knock out Ho-Oh, and my opponent chooses to use Ho-oh's Phoenix Turn and gets Heads on the flip, does the 20 damage from Dark Eyes occur before or after the "remove all damage counters" part of Phoenix Turn?

Here are the cards:

Ho-Oh: http://pokegym.net/gallery/displayimage.php?imageid=31858

Shiftry EX: http://pokegym.net/gallery/displayimage.php?imageid=11727

(Note that MD Aerodactyl has a similar Poke-body, although I haven't found it in the gallery yet.)

 

[PokePop]

Shiftry ex places damage counters "after" the Poke-Power is used.
After means after everything the power does is done.