Similarly the Ritva there says that the meaning of the Gemara is not that galus does not atone at all. Rather the Gemara is referring to exempting the relatives from avenging their deceased relative’s blood. Once the kohen gadol dies, the relatives may no longer kill him. However, he would achieve atonement for his actions by sitting in galus.
Others bring this proof from another mishnah: galus atones for accidental murder. The mishnah in Makkos 12b says that if one accidentally kills in a city of refuge, he must go to a different neighborhood or city. If the only thing that the city of refuge offered was protection from the deceased’s relatives, why would he have to relocate? This is evidence that sitting in a city of refuge also offers atonement.