Yup, you got it right Floyd. Under high pH, phosphates in the water will form precipitates. When you dose Kalk or the 1st part of 2 part, Alk, it creates a very high pH zone in the area it was dosed and forms the white cloud you see, which are precipitates, and are not really useful in the tank. At that point the phosphates are bound up inorganics in particulate form, meaning they can't be used to feed algae (or corals). In order for it to become useful for algae the pH would have to drop to around 7 or lower to break the ionic bonds and release the phosphates back into the water. In regards to rocks, instead of precipitates being an issue, it is more the calcifying organisms that went into creating the rock. The corals, coralline algae, etc. They used phosphates to create those structures, so in order for the phosphates to be released from them the pH would have to drop below 7 before phosphates could start to 'leach' from the rock and feed algae. Most rock we use would 'leach' to the point of turning to mush/wet cement over a fairly short time if rocks were leaching phosphates into the water. You could speed up this process by placing live rock in a strong acid bath and seeing how many days it takes to dissolve. The lower the pH the quicker it will dissolve, but under normal tank conditions where pH is normally in the 7.8-8.2 range it isn't possible for phosphates to leach out because that is the sweet spot where inorganic particulates and rock are stable.
It is always better to slowly add kalk/alk from something like a dripper/dosing pump instead of dumping in xx ml from a cup a day in order to avoid to much precipitation because you just end up using more elements in the water and have to dose more of other things like calcium and magnesium to make up for it. On one hand heavy dosing seems nice in that it binds phosphates and removes them from the water, it comes at a cost of more dosing of other elements back into the water and having to remove those particulates before they reach the display along with worrying about not spiking the pH in the display. It is safer and creates a much more stable system by slowly dosing over the course of a day vs once a day, and dosing so the effluent goes into a 1 micron filter sock will remove almost all of the precipitates that may form, which is how it is done when people dose Lanthanun to bind phosphates and remove then from the water. In the case of Lanthanum though the crystal structures that form when it binds can be damaging to fish gills so you always want to remove the particulates by dosing into a 1 micron sock.