It would be highly unusual for tap water to have zero TA as that would mean the water would be very acidic. And, as you noted later, the TA of the spa water was testing at 130ppm then 70ppm. Addition of acidic chemicals will lower TA over time. If your makeup water has low TA and you are not using liquid chlorine, you may need to increase alkalinity using baking soda additions. You really don't want your TA falling below 50ppm as that can lead to acidic water conditions and damage to internal components (like your heater).
If your water truly has zero CH (is it coming from a water softener??), then I would add at least 50ppm CH either with calcium chloride additions OR use some cal-hypo to chlorinate the spa with. Adding in some CH helps to minimize foaming of the water.
