It's definitely open to interpretation.
I'd probably rule it as the ability's damage is done as spirit damage in all cases. That's both for simplicity so that it's predictable what kind of damage it would do (having to change the damage type based on how many hits you get is complexity I don't care for as a GM), and also because the wording to me implies that the intended outcome is this attack is intended to do spirit damage.
But you can make a pretty solid case that the spirit damage only happens in the combined case, too. This pretty much flows from everything that comes after being subject to the condition "if both attacks hit".
RAW: It only becomes full spirit if both hits.
RAI: It doesn't make sense to only do this when both attacks hit, because it becomes a kind of reverse effect, changing the damage of the previous attack. OK you always can abstract that in that attacks your divine essence turn your weapon in pure spirit guiding it to hit the enemy with both strikes justifing that you only hit with both when this happens. But err, this is just ugly. As GM I probably will talk with the exemplar player asking what it would prefer, if he prefer to turn each attack as spiritual damage, if not if it prefer only when both hits and I would rule in this way (but I don't allow it to change the idea in the middle of the adventure whe he notices what are the enemies that it will face and their weaknesses).
I personally prefer to turn everything into spirit damage, it makes more sense to me.