It seems the compound "attabhāvapaṭilābhe" means "acquisition of self becoming" or, as often translated, "acquisition of personality".
For example, if parents, for example, allow their children to make their own decisions in life, the children will develop a personality based on their own decisions.
But if parents, for example, are very domineering & even abusive, their children will develop personalities reflective of the violence of the parents.
Or when people are brainwashed by political rulers, such as Mao, Stalin, Hitler or Obama; or by the corporate or pornographic mass-media, the acquired personalty will be reflective of this group brainwashing.
In other words, it appears the translation of "reincarnation" is very imaginative.