DICOM uses LPS coordinate system, so if you load the exported image into third-party software then you may need to choose this coordinate system for export. Use Export to files feature.
Image is specified in physical space, so the exported model is defined in physical space, too. There is no need for any further conversion. Note that “converting voxel coordinates to physical coordinates by multiplying by the voxel size” would produce incorrect results: you need to take into account not just image spacing (voxel size) but also image origin and axis directions.
This is completely normal. Origin of LPS coordinate system in DICOM files is often chosen to be near the center of object of interest, so S coordinate value is negative in half of the image.