The Transformer Rig provides visual feedback about what is outside the region of modification. Red dots show regions that are clamped (will not change), while pale yellow dots show regions that are free to move.
The Transformer Rig uses the modifiers and constraints to make an educated guess at what is outside the region of modification, but sometimes it needs help to determine this correctly.
To provide the Transformer Rig with a hint that a particular part of the surface is to be held fast, add a clamp point. Clamp points can only be added if there are targets and constraints already applied to the Rig.
A pink indicator appears where you click to show that a clamp point has been established.
If you are clamping an area that has inadvertently moved, you will see that it snaps back to its original, and proper, position.
The visualization also updates to show that the Transformer Rig has understood to hold fast the selected area of surface.