I've run kalkwasser on and off for decades. Here are my observations.
Kalk is a balanced additive. It provides both alkalinity and calcium in the basic 2:1 ratio needed for the hard coral (i.e., SPS) skeleton formation.
Details: This ratio is an over-simplication as it doesn't reflect the content of magnesium and strontium in these skeletons. But it's still a good rule-of-thumb for understanding.
Kalk (aka calcium hydroxide, or slaked lime) saturates in fresh water at a very, very low level. This limits how much alkalinity you can dose per day.
Details: 1.89 grams per liter of fresh water at 0 degrees C, down to 0.77 grams per liter at 100 degrees C. At 25 degrees C (77 F), solubility is 1.59 grams per liter. It's solubility and pH are so well known and happens at such low concentrations that it is actually considered a relatively good standard for pH calibration at high pH levels (pH of 12.54 at room temperature, 77F). It also means that, if you're not running the stirrer in your kalkwasser reactor, you may not have good control of the concentration of the solution. This is IMPORTANT. When stirred with all particulates settled out, a liter kalkwasser is saturated and, at 77F, delivers 808 ppm of calcium and 40.8 milliequivalents of alkalinity to your tank. (Of course, that's diluted by the volume of your tank). That limitation means that, when administered as part of a top-off system (that compensates for evaporation), evaporation limits how much alkalinity you can dose in a day.
This limitation may not be a factor in new systems without much consumption (i.e., calcium carbonate (hard coral skeleton) deposition / formation), but in systems with high consumption, is likely to be insufficient and will require additional supplementation (e.g., calcium reactor or two-part dosing).
For example, let's say that a 100 gallon (378.541 liters) system evaporates 1 gallon (3.78541 liters) of fresh water per day, and that you're replacing that evaporation with saturated kalkwasser. That means you're adding about 6 grams of kalk total per day - that's enough to form about 8 grams of coral skeleton (calcium carbonate) or about 3 cubic centimeters of skeleton (at most, assuming of the consumption goes to skeleton formation).
If your goal is to maintain stable calcium and alkalinity parameters (and it should be once you've reached your targets), then supplementation = consumption. That is, replace what is used. Anything more, and levels in your water will increase. Anything less, and the levels go down.
Details:You can use these "trends" in your test measurements to estimate consumption. Over the long term, if you've got corals that are growing and increasing in size, consumption will go up and demands on your supplementation methods will increase.
Following this, if you find that your levels are increasing, you need to add less kalkwasser (or increase consumption). Here's the thing, though, if you're adding it as part of your ATO and your evaporation rate is high enough that you're delivering more than is needed, then you basically need to add less kalkwasser. This means less ATO water through the kalkwasser reactor. You really can't - or shouldn't - try adjusting the stirrer on/off times. That's basically going to be a crapshoot as you won't be able to reliably control the concentration of the dissolved kalk in solution (which is one of the key reasons kalkwasser was once highly regarded in the hobby) and you're likely to see your levels fluctuate without much control. You CAN adjust how much ATO water is going through the reactor, but is you're basically running all your ATO through the reactor, reducing this (without compensating with ATO that bypasses the reactor) will only reduce your water level and raise ion concentrations (i.e., salinity).
One solution is to abandon kalkwasser for now and move to a two-part approach. Another is to add only as much kalkwasser as is needed, and to supplement the rest of your ATO with fresh water that bypasses the ATO. A third approach is to manage your parameters with water changes during this time when your tank is reasonably young without much growth, and then to switch over to kalk when things are growing more. And yet another is to increase consumption (adding larger, fast-growing corals, changing light management to increase growth, etc.). The first two approaches may require you to invest in dosing pumps, the second being very popular even today. The third was an approach used often a couple of decades ago. (It's still valid.)
To reestablish your levels, though, will require that you take your kalk reactor offline (that is, bypass it in your ATO setup) and to let your levels drift down to your target levels. If the system is small enough, you can perform water changes to help move things along.
I'm sure that I've missed a few things that I've learned over the years. But, while kalk is great (inexpensive, fairly simple, low-investment setup), I'd encourage you to look at the difficult parts of it. Namely, limited alkalinity delivery (due to low saturation level) and accidental overdosing. The first of these requires that you will eventually make additional investments in other delivery methods while the second means you'll be investing in additional hardware and complexity to manage/reduce the risk of an accident. I still hold kalkwasser in very high regard, but you should go into it with open eyes.