Yes Sir, thats distilled water!
I've heard concerns that some older condenser coils were galvanized, etc, and could poison solutions, but you have all new stuff, and typically you buy top shelf.
This will be so much better than your tap water. I've had zero issues with it as feed, or pouring back into my humidifiers.
I've never used Promix soil, but the Roots Lush I'm currently using is also peat based. It shipped oven dry, and I had to mix it with water in a 5 gallon bucket and let it sit a few days to rehydrate fully. Fill your containers to the very top, because it will pack down by itself as it gets watered and needs to be topped off.