If an EPSF object placed in a ClarisDraw document appears correctly onscreen but alignment shifts when it is printed, the issue may be in the source image.
For example, in Mathematica, images can be cropped in such a way that the actual size of the object remains the same while only the cropped image is visible. An EPSF file created from this image will include the "removed" part of the image, and if this part is invisible in its environment, the image will appear to have moved.
Solution: Recompile the image in Mathematica so that the image's size matches its visible part, and bring this image into ClarisDraw.