A friend of mine did a similar, slightly less sophisticated Monte Carlo approach to Jay's and came to the same conclusion that the control condition was far from truly random.
It is not uncommon in parapsychology for an RNG control to show deviant behavior; at the PA convention, engineer Garrett Moddel told us about how he had hoped to find psi without living things (or, as he called them, "glorified bags of salt water") and set up an experiment to see whether an RNG would show anomalous behavior "in anticipation" of being strongly disturbed; he reported a strong, clearly distinguishable spike of activity. However, this disappeared in the replication experiment. Moddel's conclusion was that, unfortunately, his positive results had been the result of an experimenter effect. Similarly, Hideyuki Kokubo and Takeshi Shimizu actually made an entire presentation about how the physical bio-pk effects they observed in their lab were still marginally present in dummy control periods both prior to and after a formal experimental session was conducted, but (importantly) not for formal control periods on different days. Their subjects had a tendency to think about their targets after and before their trials.
While the temptation is to conclude experimental error in a psi experiment when the controls don't behave precisely like the experimental targets, one really should take note of the fact that controls aren't there to behave predictably; they're there to serve as an observation from which a difference can be deducted that rules out the influence of confounding variables. Here, we very clearly have an example of 204 sessions (the vast majority of which were pre-registered), 102 of which differed from the others only by not being subject to active intention. That we observe an actual difference in the response variables for these two conditions is the anomaly. And it occurred for both the pilot and the repeat experiment.
What is certain is that these experiments require replication. IMO, at least ten RNGs should be used, and if the same patterns can be independently observed in each of them then that would be pretty compelling. Additionally, control periods should be administered both directly after an experimental session by an assistant and also randomly scheduled on different days by a computer.