WizardOfBoz

So let's refer to the locknut surfaces that touch the inside of the dropout as your "reference surfaces". Ideally, the bike rim and tire is centered between those surfaces.

As you know, if a wheel has a small section that is out of true - too far left or right - you can tighten a spoke to bring the rim closer to the reference surface on the side of the hub that the tightened spoke is on. Or you can loosen a spoke to let it move away from the side the spoke is on. What if you tightened all the spokes on the left side of a wheel? The rim would move left. If it had started out perfectly between the references surfaces, now it will be off. Still true, but too far left or right.

For the back wheel, you have a freehub or cluster. This means that the hub flange is moved toward the centerline of the hub on that side. If you centered the rim between the hub flanges, it would be too close to the non-drive-side reference surface, and too far away from the drive side ref surface. So you typically leave the non-drive side spokes a little loose, and tighten teh spokes on the drive side. This moves the rim towards the drive side. By adjusting the relative spoke tension on the left and right, you can center your rim. This process is called dishing.

If you add spacers under the locknuts, you are moving the reference surface on that side, and so if your wheel is dished properly (e.g. centered) initially, after you add the spacers you will a have improperly dished wheel. So you need to tighten all the spokes on the side you add the spacer to. (A little bit, then check. And if the DS spokes are already a bit taut, you could loosen the NDS spokes. )