The positive correlation between creativity and Eysenck's Psychoticism trait, also implies a positive correlation with the more specific Schizotypy trait, and a negative (inverse) correlation with Big Five traits of Conscientiousness and Agreeableness (and Agreeableness is essentially identical with Simon Baron Cohen's Empathizing trait).
The inverse correlation of Creativity in terms of C and A is understandable, and necessary - once C and A are properly understood.
Creativity implies a strong ego, a person who looks at a situation and comes up with something different because he believes it possible - even probable - that he knows better than other people, and is (to some extent) indifferent to the opinions of others on this matter.
Conscientiousness is sometimes conceptualized in terms of delayed gratification - the ability to put-off gratification now, in return for greater gratification in the future. For example, to defer the pleasure of playing and instead study academic subjects - forgoing current pleasure of play, and suffering the tedium of work, for a (hoped for) greater pleasure in the future.
But this is an error - because it is not the way the mind is motivated. The mind actually works by maximizing current gratification - by doing what is positively rewarding, and avoiding what yields negative emotions.
Therefore the proper way to conceptualize Conscientiousness is that a high C person gets more gratification here and now by doing what they feel is best to do, or necessary to do, or which they have been told to do by an authority, or what they are supposed to do according to peer pressure.
Therefore, high C implies a high degree of concern for internalized social norms - a tendency to feel good (here and now) when conforming to these social norms/ values - and/or a tendency to feel bad (e.g. guilty, ashamed, afraid) when transgressing or failing to follow these social norms.
This is what links Conscientiousness to Agreeableness or Empathizing - a dominating concern with the views of other people - attention to knowing the emotions and wishes of others, a calibrations of one's own (observed or perceived) behaviours to stay in line with the expectations or desires of others.
So, it can be seen that Conscientiousness and Agreeableness are two side of the same coin (and the inverse of Psychoticism) - which is that a person high in Conscientiousness and also Agreeableness is one who - here and now, and in the present moment - derives the greatest satisfaction from his conformity to the social group, and is attentive to cues of social group values: and (more important) who has aversive feelings if transgresses or he fails to follow social norms, such as would happen if creativity thinking was in play.
And such a person is not creative - because he is focused on learning and doing what the social group wants him to do, and is dominated by such concerns.
Note: As described elsewhere, and in line with Gregory Clark's description in A Farewell to Alms - I believe that higher-C, higher-A were positively selected-for in the context of complex agricultural societies - where high-C, high A (and also high general intelligence) were economically useful; and where individuals with high-P traits would have tended to die from starvation or disease - or were differentially killed as being vagabonds, criminals and outlaws.