Rigify moving and posing, origin doesn't seem to move When I Rigify a model, pose it in a scene and move it around etc.
The model seams to remember the "origin position", from when I created the character.

(mesh origin as in blender terms, this is a property of a mesh)

When I then want to edit the rig, or mesh.
I put it into "rest position". 
Then it jumps back to that original position. This is a bit frustrating in large scenes. Apparently I moved or posed it wrong.

Or is this normal behavior?
An armature moves the mesh data of an object, not the object itself. If you make the armature the parent of the mesh object, the mesh object will move with the armature when you move it in object mode. You will also notice that adjusting the armature in pose mode will leave the origin of the armature at the start position.

The modifiers have some display options that can be turned on/off. Some modifiers only have two some three and some four, the armature modifier has all four. Enabling all four will prevent the mesh snapping back to it's original position in edit mode.