That really doesn't make any sense. Lots of things pool store people say don't make any sense.the "good" chlorine and the "bad" chlorine need to strike a balance otherwise they will push into a serious chlorine demand
You should start trusting your test results, and not theirs, quite soon. With just a tiny bit of practice a novice with the TF-100 gives better test results than most pool stores.
There are a couple of things about your TF-100 test results that I am curious about. The TF-100 measures FC and CC with the FAS-DPD test (powder turns the sample pink and then drops eventually turn it clear again), and TC with the OTO test (inside the blue inner box). You list FC and TC results, but not CC. Which test did you use and how did you write it down? Also, you list an Adjusted Total Alkalinity value, but the TF-100 measures plain Total Alkalinity, without an adjustment. You should write down the Total Alkalinity result directly from the test kit, and not do any adjusting.
Yes, your PH is too low. You want to raise PH to at least 7.2 fairly soon. This time, add less chemical at a time, give it an hour to mixin, then test again and continue adjusting from there, so you don't overshoot.