It is often noted that with replacement reincarnation, the personality undergoes drastic change. This would be a strong indicator of such an experience.
I think that Jung makes an excellent distinction in the above quote with regards to the differentiation between the psyche, what I would refer to here as the "body-mind", and the soul, which he equates to/with personality.
I have experienced this distinctive line in my own inner work with healing using essences. The psyche is what is affected. Whatever needs resolving in this area gets resolved so that my soul can integrate more, therefore the personality "evolves" more, so that everything falls into alignment. In this way integration and Wholeness are achieved.