I have a rig, and when I select the Armature or the Model, and go to edit mode, they move position. They just go to the left, and they come back in object mode.
In Pose mode make sure you are in "Pose position" .
In rest position it will go to the objects original position and origin point
Also , Edit mode doesn't effect the animation / Pose , so when you go into edit mode , the armature will also go to the objects original position and origin point . Edit mode is only for moving vertices/faces/edges and bone origin placement
I had this same problem too! I tried all of these answers but none helped, I finally figured it out. All you have to do is go into pose mode and select each bone individually(you might be able to select all but I didn't try) and press "Ctrl+A" and apply location, rotation, and scale. If this doesn't help for you I am very sorry. It worked for me.
Unless it's some really weird placement, then what you describe is how it's supposed to be =) What you see in edit mode are the default positions of your bones. In other words, where your bones will be if you reset the position/rotation/scale in pose mode.
Apply all the modifiers, which you have, such as subdivision surface, solidify etc.
Then do the "With automatic weights" all bones will be in the correct places.
I think it is simple sir please click on the armature and then find Reset Position and then click on that.
While you pose again click on pose position.