I wouldn't go so far to say that it is impossible but your saying that your DK went up to 12 but all else remained the same? I could be wrong, but I don't see how that is possible. By saying that your alk is 4, you mean that it is 4 meq/l (milliequivalents per liter) and by saying your KH (DKH) is 12 that would mean you have an ALk of 12 degrees of carbonate hardness. These are two different ways of measuring your alk and they seem pretty close to correct (technically if you have 4 meq/l you have 11.2 DKH) Anyway, my point is that these are just two different expressions of the same thing, if one value changes, the other one does as well because they are the same thing. Might want to double check you test method.
The desirable way to run a CA reactor is to put a ph probe in the reactor to regulate the ph inside the reactor and have the controller turn on and off the flow of CO2 VIA a solenoid actuated regulator as is needed. You technically could put a probe in the sump to regulate but this is a riskier and less reliable method. Also, the manufactures recommendations of how much CO2 should be injected is not very reliable. The demand for calcium & ALk is determined by the load (population of organisms using up carbonates) not by the volume of water. Even set up properly, it can take several days to weeks to get it dialed in properly, this is definetly not a "set it & forget it" devise. In my opinion, you should shut it down untill you have the proper equipment to operate it and better knowledge of how it works. At that point, get it up and running while your going to be there like on a weekend where you can watch and test what is happening.
Joel