Whenever creating a MASH network (both Instancer or Repro), the source object's pivot point is ignored. Instead, each MASH point acts as its instance/repro's pivot point. However, you can give your objects pivot points that are represented in MASH using the following steps.
To give objects a pivot point that will be represented by MASH
Once you've done this, you can make further adjustments to the mesh within the group node to affect its pivot in MASH.