I would test several taps to assess your situation with a water softener. For example, my water softener is tied to my internal water supply as well as to my 3 external water bibs. So my fill water is softened. I have one other tap that is on the pipe going into the softener. I can connect a hose to that to fill my pool with non-softened water.Should we test our water prior to fill? I am unsure if our hose bib is supplied by softened water... would I be able to tell from testing the water? Should I just plan on bypassing the water softener before we fill just to be on the safe side?
So my suggestion, is to test your internal tap at the kitchen and bathroom, test 1 or all your external bibs and then determine if you have a tap prior to your water softener and test that. It would be best to do your initial fill with the non-softened water because your water softener will regenerate after 3000 (or so) gallons. So you would not have softened water going to your internal water supply during this regen process. This is why most water softeners are set up to regen at 2am or so in the morning when your internal water demand is near zero.
You need to test for CH on all, you can also test for TA and FC. Your FC should be 1ppm or less. Your CH for internal taps should be zero if your water softener is working properly. Any external tap that matches to your internal taps is then also connected to the water softener.
Hope this helps.