Which is the physical insight behind the widely approved 'space vector' notation used in the analysis of the dynamic model of electric machines?
Perhaps your difficulty is that the frame of reference or the "space" containing the magnetic flux and force vectors is rotating rather than fixed to points on the structure of the machine. In induction motors, the frame of reference rotates with respect to both the stator and the rotor, moving at the synchronous speed with respect to the stator and at the slip speed with respect to the rotor. In synchronous motors, the frame of reference is fixed with respect to the rotor, but rotates at the synchronous speed with respect to the stator. Thus the vector representations of the fluxes and forces have fixed positions with respect to the phase-vector representations of the AC voltages and currents.

I believe that this representation is developed by first examining the vectors with respect to the windings in the machine without considering the motion of the rotor and then examining the machine operating at a steady-state speed.

Equivalent Circuits

The analysis and control of electric machines makes use of equivalent electric circuits that are mathematically analogous to electromagnetic machines. They have a basis in physics, but that basis may not be as firm and direct as you might like. Engineers generally use the tools that will provide answers with a level of accuracy that is suitable for the ultimate purpose. Scientists strive to explain the laws of nature as thoroughly and accurately as humanly possible. Engineers strive to design products that are useful to human endeavors and economically affordable.

Terminology

Not all engineering terminology is carefully thought out. Even terminology that is carefully created is often simplified in everyday use. As a result, some terminology can have more than one meaning depending on context.  I suspect that engineers are more tolerant of imprecise terminology than scientists may be.