An aqueous ink printer includes a moisture applicator that applies moisture to a side of a substrate that is opposite a side that bears or will bear an ink image. The moisture applicator includes a switching network that is configured to independently and selectively bias the tile segments electrically. The tile segments contiguously cover a surface of the roller. As the switching network is operated to electrically bias the tile segments using data corresponding to the ink image, they transition from being hydrophobic to hydrophilic so the electrically-biased hydrophilic tile segments attract moisture from water in a trough or from water vapor produced by an ultrasonic transducer in the trough. The moisture is carried by the electrically-biased tile segments to the substrate at areas where the amount of ink in a portion of the substrate on the other side of the substrate exceeds a predetermined ink coverage threshold.