Essentially the way Aquamist works is you have a couple of additional injectors that shoot water instead of fuel. There's a water map in an ERL MF2 injector controller. The same controller can be used to map additional injectors. F-max actually includes it, pre-mapped, with their turbo kits.

Anyway, the amount of time the water is in the intake is too short to have any sort of cooling effect. As soon as it comes out of the injectors it gets sucked into the motor. The reason water injection lowers cylinder temps is that water has a very high specific heat. It takes a lot of heat to evaporate the water, which means that it can absorb a lot of heat. So when the water hits the cylinder, it is vaporized almost immediately. Some of the heat inside the cylinder is used up to do this. When the effect is taken cumulatively it helps keep the cylinder temps down.

Water injection does work very well as a detonation aid, and it does let you run more boost. It does not however, prevent heat soak from a compressor running for extended periods of time and does little to help cool the charge air.

Ideally you want both an intercooler and water injection. The intercooler would cool the charge air, which then makes it more dense. More dense = more oxygen to combust and the ability to combust more fuel with it. More oxygen and more fuel = more powerful explosion. More powerful explosion = more power. It also however, means higher cylinder temps. Add water injection and you can cool down the cylinders.