I too had the same problem with my pervious '91 P10. But, my 93.5 does not in any way act in this manner. I too do believe that the central locking unit on this car needs a bit of refinementT4 Primera said:The following has worked for JDM Primeras before.
Find the central locking control unit in one of the front kick panels. Mine had "door lock timer" written on it and was a black box about the same size and shape as a cigarette packet.
Unplug it and clean the harness contacts. See if it makes a difference.
The above worked on one car but mine needed the control unit replacing - about NZD65 for a 2nd hand one.
Hope that helps. =)