Reflexive cues -- REALLY fast ones. Faster than any possible voluntary motor repsonses. AND with a resulting control phase lag that is both unavoidable and NOT trivial.
If you go back and re-read those studies, I think you'll find that they mean that action precedes cognitive
decision. Non-verbal desire and intent precede the cognitive awareness (i.e. the "verbal" thinking part of your brain that "talks" in your head) that you desire or decide on something. Intent is way ahead of "you."
This is when it starts getting very interesting to me. There is certainly a part of precognitive process that determines how you arrive at a certain state in life. Why are dung beetles obsessed with rolling dung? Why do humans obliviously reenact certain habitual patterns, again and again? "We're made that way." Might be the best answer we can come up with, but we very rarely observe it in action. Only when we have some kind of cognitive dissonance and are forced to reconsider things.
There seems to be both a subjective consciousness and an objective consciousness shown in that study. Some more primal, underlying part of you exists and creates the essential ground that your subjective self runs around in, so to speak. Our programming does seem to arrive from afar.
When many creatures- including humans- are deficient in a nutrient, they crave food that contains it, even though they have never attended a class in nutritional chemistry. I don't know how that works, either, but I think it's the same way.