This is a property of self-distillation.
Self-distillation shifts the behavior of the model towards that of the model + steering. As such, you don't strictly "need" the tokens to be in-domain for it to work. The logits are a vessel for transferring the steering into the model's internals.
The tokens can be gibberish. What transfers isn't whether they're gibberish or not, but how the flavor of model predictions, if given gibberish, differs from that of an unsteered version of itself.
In this specific case, the behavioral difference comes from the "temperature-shifted, truncated samples" in the "teacher" sampling strategy, and it is that difference that is internalized by the "student" model.