In this article it is argued that it is difficult to explain the finding in the physicalistic framework, and that the allowance of free will seems only to worsen the situation since precognition of acts of free will does not make sense. In the framework of Topological Geometrodynamics (TGD) zero energy ontology (ZEO) replaces the standard ontology of quantum theory. ZEO predicts that in "big" (ordinary) state function reductions (BSFRs) the arrow of time changes and that the identification of acts of free will identified as BSFRS is not in conflict with the determinism of classical physics as an exact part of quantum TGD. Also Libet's findings can be understood.
This suggests a model for the anomaly. The experiment would have already happened as BSFR ("already" is with respect to subjective time to be distinguished from geometric time) for a quantum system associated with the experimenters and participants. The knowledge that the event is actual inspires unconsciously the attempt to "remember" the personal performance in the experiment instead of only imagining it and this would explain the improved future predictions.
See the article Why the outcome of an event would be more predictable if it is known to occur? (with Reza Rastmanesh) or the chapter About the nature of time.
For a summary of earlier postings see Latest progress in TGD.