A possible explanation - but from a controller's perspective only (not an engineer)....
In processed radar systems a position symbol is usually only presented to the controller when the radar boxes decide that there really is something there. With PSR the radar will think something is real when a certain number of updates show a target moving in a way that is consistent with an aircraft (I think that the characteristics of the return are also assessed in some systems).
When the radar has decided 'it' is real it will create a track and put a position symbol on the display. It will then start to predict where that target is likely to be on the next update and, if it finds a return in that position it decides it's the same aircraft and displays it to the controller.
All of this electronic trickery is to minimise the presentation of false targets, reflections and all of the other things that used to make radar displays look messy.
To help the controller to keep the identification of each target it is possible to associate a label with a particular track. The problem is that if two or more targets get close to each other it is possible for the radar to confuse which target should have which label and you can get track/label swap. Unfortunately the nice labels associated with PSR returns on a nice clean display look very much like the picture you get with SSR and it is easy to be lulled into a false sense of security and to think that everything is exactly as it looks on screen but if you have PSR only there are many potential gotchas to catch the unwary.
So track jumping may be a problem within the radar processing system......or, maybe something else completely.