Could be some kind of Zero space broadcast. Maybe quantum-entangled particles. The Pemalites were a space-faring race, meaning they'd have to communicate across the galaxy with who knows how much matter in the way. They were working with technology given to them by the Ellimist, whose networked brain would depend entirely on having a sophisticated, reliable, and instantaneous comms array. In fact, his network worked so frigging well, it was still transmitting and receiving from both sides of a black hole's event horizon, thus turning him into the Ellimist we know today. That means it's definitely not operating on any electromagnetic wavelength within our three dimensions. I don't think a measly three miles of water would pose any kind of problem for that.
