If your water comes from a municipal source and not your own personal well, it's treated with chlorine. No mystery there.
You have extremely soft water -- it didn't come out of a water softener, did it?
If that's what comes out of the hose untreated, then you'll need to add some Calcium to protect your fancy pebbletec finish and some baking soda to raise TA to roughly 60. It doesn't have to be exact -- if it comes out to 9 lbs and you buy it in a 10 lb package, add it all. If it calls for 11 and you have 10, close enough. After that's had a chance to mix, then adjust pH using acid. As you've seen, small acid additions make huge pH changes when the alkalinity is low like yours. And then of course, CYA and chlorine need to be added. And then when everything is nicely balanced, you can add salt. Lastly you turn on the SWG. But this is all if. Make sure that the fill water isn't going through the softener, because if it is, the softener won't be able to sustain the flow to fill the whole pool.