Position of the long rod bushing is going to depend to some extent on riser design. With an expensive (good) riser and long rod you would expect the rod the be at least parallel to the bow plane and close to it. Perfection ... nobody can afford
. Bear in mind that if the cog of the stabiliser system is not in the plane of the bow then torque will be generated by the bow recoil so if the rod is a long way out then some action will be required. (This happened to me once where the two threads of a V bar bolt were not square - a lot of head scratching went on until the penny dropped)
The alignment IMO anyway should be good enough to use the long rod for limb alignment and for checking any riser twist when drawing the bow (or checking bow hand position re riser twist, other side of the coin). As regards centre shot the arrow should be almost parallel to the riser (within its radius anyway with a typical rod diameter. "Almost" is however not a good gauge. Would use the string to set up centreshot (although you can use the rod as a guide to the alignment of the string).