Onix's Energy Healer + Rainbow Energy

[Imperial]

If you attach a Rainbow Energy to Onix (Unleashed 56) does his Poke-Body kick in first, removing no damage, or does the Rainbow damage counter come first, allowing Onix to remove it?
The errata matches up the phrasing to be "When you attach this card/an Energy card from your hand to 1 of your Pokemon/Onix, put/remove 1 damage counter on/from that Pokemon/Onix."

 

[PokePop]

When two effects are triggered by the same event, the owner of the Pokemon being affected gets to choose the order they are applied.