Bugs related to this problem have mostly been fixed since eexpmap 4.6.1 of xmmsas 9.0.1. eexpmap should now produce exposure maps in DETX/Y that match input images exactly. The single exception is when the event list from which the input image is made contains any PN event with RAWX=28 and DETX=5476, or with RAWY=72 and DETY=9588. The DETX/Y values in these cases actually lie outside the RAWX/Y pixels. Removing these events, reassigning their DETX/Y, or turning off randomization will all solve the problem.
To produce exposure maps in sky coordinates that match input images exactly, users should call eexpmap with the parameter attrebin set to at most radian, i.e., attrebin=0.020626481 (arcsec) or smaller. For long observations, this could prolong the running time of eexpmap substantially. However, exposure maps thus produced will match the input images exactly. Doing the same with older versions of eexpmap will also help to reduce, but will not completely eliminate this offset.