Most likely your Rhino is set up to create extrusion objects for thins like boxes, cylinders etc. (as well as extruded planar curves). One clue is that extrusion objects do not show isocurves as you remarked. If you check properties for the object, it will also mention the fact. Extrusion objects are special “lightweight” Rhino objects and their meshing parameters do not respond to the normal mesh commands.
In order to get your extrusion objects to respond as you would like to meshing, you need to convert them back into polysurfaces. You noticed that moving a control point does that, however this is not necessary. Simply call the command ConvertExtrusion on your selected extrusion objects, that will turn them into surfaces/polysurfaces.
If you would like to turn off automatic the extrusion creation behavior altogether, Call the command UseExtrusions and set it to No. That way when you make a box, it will be a polysurface from the start.