Back movements do not alter perspective (perspective = referred spatial relationships of observed objects.), only alter the 3D > 2D rendering of shapes and frame position within the IC cast by the lens. The Front standard shift, rise or fall movements will alter perspective, and the tilt and swing movements may alter perspective or not depending on camera design, however they generally do not render a change in the 3D>2D projection shape as the rear standard does, though again this can be slightly effected based on camera design. So, the simple rule is you use the rear standard tilts and swings to correct visual geometry; the rear standard shifts, rise and fall to correct framing without altering perspective; front tilts or swings to alter the PoF (Plane of Focus) without affecting projection geometry; and the front shift, rise and fall movements to make fine adjustments to perspective.
Since we want elements seen in *flat* stitching frame captures to line up, we need them to all have the exact same perspective, which in turn means renders them free of any "parallax." (Parallax = apparent displacement of an observed object due to a change in the position of the observer.) Hence, for flat stitching with a tech camera, it is always best to use rear shift, rise or fall movements.
Spherical sticthing is another discussion. As indicated above you need to pivot the entire camera and lens assembly around the anti-parallax point (technically the entrance pupil of the lens) to maintain frame perspectives that line up.
