First off, I am not a chemist, so take anything I say with a large grain of salt. I reviewed the treatment document, the one thing I noted is that lime is added to the water, then they re-acidify the water with CO2 early in the treatment process. I suspect that the water when it comes out of the tap it is not at equilibrium (for example my tap water can sit for days without the pH changing), in particular the water has too much lime and perhaps too much CO2.
I suspect when the water is at normal temperature and pressure it degasses some of the CO2 from the water causing the added lime to precipitate out. Under these conditions the pH of the water will be controlled by the relationship of the lime, CO2, and temperature of the water. But with material leaving the water, both the lime and C02, the pH changes overtime. The precipitated lime would be the white dust in the buckets. I am not entirely clear what would happen to the pH when both CO2 and the Lime leave the water at the same time.
What this means to you is that it is probably best to age your water to allow for the pH, GH, and KH to stabilize before using it for your fish. Additionally, you will still have to treat the water for Chloramine because that has been added, chloramines do not de-gas out of the water like straight chlorine can. Another interesting point is you have Floride added to your water, I honestly don't know what the implications for that are, both in its effect on the fish or on the water chemistry.