If you dose with kalk, to make it effective you need to use a kalk reactor. A dosing pump just doesn't do it unless it feeds a kalk reactor. You can run all the ATO water through the kalk reactor. As I mentioned, it's really hard to overdose it.
You would feed the water from the ATO pump into the reactor and from the reactor to the return point in your system, usually the sump. Kalk reactors are sealed to keep out air. If you let mixed kalk water sit around in air any length of time, it's much less effective. Much will precipitate out.
The other way you can dose kalk and have it be effective is to use RO/DI water, and mix just the amount of kalk water you need that day and add it to you system. This works but is a pain to do because this method needs to be done daily. That get old fast.
While we are on the subject, test your magnesium level. If that is low it's very hard to maintain the calcium and alkalinity balance.