All Axes Constraints are solved during the Orientation stage of Processing. These Constraints are typically used in single photo projects but can be used in multi-photo projects also (they act on a single photo at a time).
Note that during the processing of a multi-photo project, normal optimize runs without the axes constraints being used at all. When the optimize is complete, the axes constraints are reviewed to see if any objects need to be forced to lie along certain axes or planes etc. This means you can have some objects (points, lines, edges) appear on only one photo of a multi-photo project and they can have computed 3D positions if they are constrained by one of these constraints.
Note also that the axes constraints allow some limited Inverse Camera solutions (solving for focal length and principal point) on a single photo if the perspective is strong enough. To solve focal length you typically need a strong two point perspective (that means vanishing lines in two directions (x and y axes for example)). To solve focal length and principal point you need strong three point perspective. See the Working with Unknown Cameras and Photographs section for more detail.