AFAIK Newcomb's dilemma does not logically contradict itself, it just contradict the physical law that causality cannot go backwards in time.

It certainly doesn't contradict itself, and I would also assert that it doesn't contradict the physical law that causality cannot go backwards in time. Instead I would say that giving the sane answer to Newcomb's problem requires abanding the assumption that one's decision must be based only on what it affects based on forward in time causal, physical influence.