I was just reading up on bermuda and your water tanks.
http://www.bermuda-online.org/architecture.htmSo rainwater runs off the roof (which is whitewashed) and runs into the holding tank(s). Some lime leaches out of the roof paint and you may get heavy metals and other pollution if the roof is dirty or pipes from the roof are rusted or corroded or leaking. If galvanized piping is used in an older property, it will deteriorate and corrode internally due to the "soft" rainwater. You're supposed to disinfect the water using 2-4 ounces of bleach for every 1,000 gallons of water in the tank.
Here's another interesting article that says you may have a high bacterial count of e-coli.
http://www.mercuryexposure.org/index.php?article_id=214I don't think I'll grump about our local water company any more!! LOL
You water conditioner has something that binds heavy metals right?
ok... so your water starts out soft cuz it's rainwater and the pH is so high cuz of the lime from the leaching of lime from the roof and concrete.
From what I understand, rainwater tends to soft (low in minerals), more acidic, not well buffered and contain lots of CO2. but you get splashing as the rain hits the roof and more splashing as it enters the holding tank which should gas out some of the CO2. The cement in the holding tank will raise pH cuz it leaches lime into the water. Dunno about the sludge at the bottom of the tank. How active it is in producing gasses, probably depends on how chlorinated you keep the water in the holding tank. If it's well chlorinated there shouldn't be many bacterial processes happening that would produce gasses. If it's not, you'll have a lot of gasses happening, the type depending on how well oxygenated the sludge area is. I also wonder how much fresh air circulates in the tank and how much water movement happens in the tank.
I still have no idea of why pH would decrease when you agitate the water.

Either something's gassing in or something's gassing out when you shake it. but gassing CO2 OUT of the water should RAISE pH, not lower it.