It seems the 12 seconds is simply a resultant thing from the fact that at least the WXR-2100 needs 11.2 seconds anyway to complete a sweep cycle in windshear mode. By the way, display sweep and antenna sweep are nowadays independent as the display sweep is done out of memory.
The following is what the manual says about some of that topic:
The total time required to complete one cycle of the MultiScan process in all modes except windshear is 8 seconds. When in windshear mode, the total cycle time for both MultiScan and windshear is 11.2 seconds. Thus, there is no significant change to observed weather during one cycle of the MultiScan process. What does change is the relationship of the aircraft to the weather. To compensate for this, MultiScan translates (figure 3-8) and rotates (figure 3-9) the stored digital image to compensate for aircraft movement.
The result is that the Collins MultiScan updates all radar displays every four seconds in all modes except windshear, in which case the displays update every 5.5 seconds. One interesting element of this process is that the antenna scan is no longer tied to the display sweep. This frees the antenna to perform multiple functions without interrupting the pilot’s weather presentation.