How do ATC radars know where to position a primary target?
Primary radar, even modern digital systems, do not give any possibility to the controller to determine altitude.  The digital system has that capability, but civil ATC does not.

In primary radar displays usually just the azimuth and range are plotted. So an aircraft at 15.000 ft 9.5 NM away will be plotted on 10 NM distance, just like an aircraft at 0 ft 10NM away. Usually the secondary radar is collocated with the primary so secondary targets can be displayed using the same projection (disregarding the altitude). 

If you now apply horizontal separation based on this projection, you will never bust the separation minima. It is a conservative way of providing separation, but when there is no altitude information it is the best possible way. 



Note that this does not only apply to primary targets, but also to Mode-A only targets