I think you may have taken this the wrong way:

i

But when taken in concert with the blessing itself from in game:

i

The chance (the operative word here) goes away when it procs (thus beginning the one turn cooldown) and simply means EACH multi hit has a chance to proc Phantom Touch bonus damage but goes away once it procs. It's working as intended and I think it's made fairly clear in the description.

Furthermore, Phantom Touch has a chance to do a second instance of bonus damage at 6*, which is another clue towards Phantom Touch not being insanely broken and ripping through FK shields immediately :D

That's where it confuses me. On multiple targets, I understand that it deals one instance of Bonus Damage, that's clear.

But in case of multi-hits hitting the same target, it's unclear. "Chance" is the operative word, but at 100%, it's not longer a chance, so if we take it out of the equation, we are left with "Champions deal Bonus Damage with every hit of a multi-hit skill". 

Warmaster, for example, clearly states that "Bonus Damage can only occur once per Skill....". 

I chalk it up to a lesson learned, but I don't know if anybody else may run into that issue in the future. 

To clarify, I was trying to marry chance + cooldown to show that proc'ing once means we trigger the cooldown. otherwise it would be terribly broken. 

Sorry you didn't get clarification on that earlier, though. 

Gotcha. Yeah, the coldown was another issue when I was trying to make 5* PT Shamael. But I feel like it's slighty different. One turn cooldown means that after the turn, it canno proc (counterattacks, ally attacks etc.) But during the turn, it seemed like Giant Slayer mechanic. 

In fact, Giant Slayer states that "Bonus damage can occur on each hit of a skill....", which also is confusing and virtually identical to PT description. 

Now, it got me wondering: Giant Slayer can proc more than once per skill, right? Or is it the same as PT?

yes, giant slayer is able to proc multiple times from a single skill.

Thanks. I thought so, but now going through these definitions, it got me questioning myself lol.