Just leave them grow where they are. The limiting factor for how many pounds of potatoes you get is the amount of sun the leaves can collect and use to fix carbon (to make starch, which they store in the tubers for energy to produce next year's plants. Growing out the side will help that, the bushier the better.
Though potato tubers are in fact stems, as SS noted, they do not produce potatoes directly off the stem, but rather produce side stems to grow horizontally and then swell at the end to produce the actual potato. Burying the stems just puts the potatoes into layers in the tower instead of a single horizontal layer underground.
A tower might yield a slightly higher harvest per square ft than growing the plant in the ground, I think this could be mostly accounted for by the additional mulching and watering people tend to do with the towers. Potatoes in a row in the ground are incredibly productive (that is why they are fairly cheap in the market). My advice is "don't sweat it", just let them do their thing, those plants have been producing well for centuries without anyone fussing over them.