Subliminal messaging.
The glowing eyes are in fact a projection device. The psi's nervous system instinctively analyzes which features in the field of vision are in focus. The retinal cells broadcast monochromatic light directly outward toward the terrain they would normally make an image of, using an ommatidium-like construct. Most of the time the retina is dark, so sight is normal, and calibrates the projected image locations precisely.
The visual association area is co-opted to create the images to be projected. These images are, by and large, written words. The target of the attack sees these words for thousandths of a second and interprets them subconsciously in the same way as they would read any other text.
The trick is that the visual projections are timed in such a way as to entrain the victim's alpha wave rhythm. The victim's brain is at a particular microsecond after processing the text when it is most vulnerable to suggestion, when the text appears again, and by a weakness in their cognitive processing, they tend to view the projected words as their own thought rather than something coming at them from outside. As a result, they tend to comply with most reasonable commands. Of course, if something is so drastic that they would start thinking why would I ever think such a horrid thing?, then they will reject it with some emotional perturbance, and the spell will be broken.
Also note that entraining the alpha rhythm in this way, so that the flashes of light come at a point where the victim doesn't perceive them as external, also means he doesn't perceive the psi as having glowing eyes. Only a witness out of range of the effect will see it.