It's currently not randomized at all. If your army has identical morale, then the same unit will always get the bonus. Actually, scratch that, the same unit position will get the bonus. If you change your unit order, you can change who gets it.
I wouldn't be at all surprised to find that Onslaught/Adrenaline work the same way, it seems to be deliberate. It could be randomized, but without a clear indication that it's supposed to be random, I'm not sure if that would be straying from bug fixing into modding. What does the tooltip say about how it's supposed to be applied?
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