Yes, the constellations on the Starfinder charts will shift if you observe the night sky from further south. The Starfinder charts are designed based on a specific latitude (in this case, around 34 degrees north), and the visibility of constellations changes with latitude.
As you move further south, more southern constellations come into view, and some northern constellations may dip below the horizon. For example, constellations that are prominent at higher latitudes might be less visible or not visible at all from lower latitudes. Conversely, constellations that are typically not visible from 34 degrees north might become clearly visible as you move to lower latitudes.
In summary, observing the night sky from different latitudes will indeed result in a different view of the constellations, and using a Starfinder chart specific to your latitude will provide the most accurate representation of the night sky you can observe.