The issue is most likely that you're applying cream to completely dry skin. The cleanser does clean well, but it strips away the protective lipid barrier from your face, and your skin loses moisture within minutes. Cream applied to over-dried skin can't fully restore the water balance - it's more like sealing in moisture that's already been lost. Hard water doesn't help either; it makes cleansing more harsh.
Try applying cream while your skin is still slightly damp rather than completely dry - this significantly improves how well it absorbs and how effective it is. You can even gently blot your face with a towel instead of rubbing it dry. Or add an extra step: after cleansing, apply a toner or facial mist, let it absorb a bit, then apply the cream.
Also pay attention to the cleanser itself - it's possible it's too drying. If you can, try switching to a gentler cleanser, at least for your evening wash. And yes, if your tap water is genuinely very hard, a filter or even cooled boiled water will help. But most of the time, the order and speed of applying your cream is what solves the tightness problem.