Time-resolved metallographic optical microscopy techniques are used together with magnetic domain imaging to clarify the interaction between magnetic domains and twin boundary (TB) motion in magnetic shape memory NiMnGa single crystals. The magnetic field and stress induced magnetic domain formation is imaged by a magneto-optical indicator film technique. Reversible TB motion is visualized up to high actuation speeds. From domain observation at adjacent crystal surfaces the fundamental volume magnetic processes during strain and field induced TB motions are derived. For magnetic field induced structural reorientations a concurrent absence of magnetic domain wall motion is found. In contrast, for strain induced reorientations processes, a complete rearrangement of the magnetic domain structure by the moving TB is observed. Dynamic actuation experiments on TB motion reveal non-linear time effects on TB mobility. In addition to training effects, the maximum field induced strain increases with actuation speed. Both effects can be interpreted as the interaction of moving twin boundaries with local non-fixed defects. The summarized results provide key information for the understanding of the connection of magnetic and crystallographic domains in magnetic shape memory alloys and for the optimization of devices for future technical applications.