Does your city water have chlorine and/or chloramine in it? Test the FC/CC of the fill water first. All municipal water will be chlorinated and/or chloraminated for disinfection. If so, you should dechlorinate the water sample first. That can be as simple as filling up a clean container of water and letting it sit in the sun for a few days. Chlorine can sometimes interfere with metal testing and so you really want to look at water that has no chlorine in it. Also, if your municipal water supplier adds any kind of scale control chemicals (typically orthophosphates), then that can skew results as well.
Ferric iron (Fe3+) almost always will precipitate out of solution as rust stains and ferrous iron (Fe2+) is typically very low in concentration. That test kit will only detect dissolved iron, Fe2+, and so you will only get part of the answer.
Perhaps you should consider getting an independent water quality lab to test two water samples - pool & fill. Labs often use mass spectrometers to detect trace metal levels as that is a more sensitive technique and immune to a lot of the interferences and cross-contaminations that can cause issues with liquid reagent testing. I believe you can get some very wide ranging analyses done for around $100-$150 depending on what tests you request. Look online as there are many vendors for such testing.