I probably would measure just once a day and dose accordingly. There might be enough noise in the alkalinity measurement to make a bit of an effect, and night vs day consumption rates might be an issue, as well.
Precipitation would happen shortly after the supplement goes into the tank. It might be in the form of small crystals (tiny particles of sand), though. Such small particle could measure as alkalinity on a test kit because the acid titration might dissolve the calcium carbonate.
You're still using the sodium bicarbonate formula with a dripper? Is the sand showing any signs of clumping?
If the dripper is rinsed between uses, it should be fine for both supplements. If there's precipitation happening, I suspect it'd be inside pumps at this point, but that's just a guess. I probably wouldn't worry much yet, although I'd keep watching.
I am using the same dripper to add both the alkalinity and calcium solutions and the alkalinity solution was noticeably cloudy today. I am wondering if it would be worth making a devoted dripper for each supplement, might be overkill but I am trying to be extremely cautious at this point.
I would measure the dKH in the morning to see how it's dropping overnight, and work from there.
Maybe try putting a fresh gallon or two (Or however much you want to work with) of salt water in a container and try adding enough alk additive to raise 1 or 2 dkh. That way you will remove all variabes from the tank. You will then know if there is some sort if issue with the additve or if the tank is consuming it nearly as fast as you are putting it in.
Are there any signs of precipitation in the bucket? Any fine powder in or buildup on the bucket? What was the dKH before and immediately after dosing?