A few things you could do to fix this:
1) set the origin of the fbx file you imported to it's own geometry.
You can do this by going to object > transform > origin to geometry in object mode with the object selected.
2) you can set the object to be it's own user.
This is a fix for an error caused by linking objects from other scenes. Somehow your ...
I had a similiar Problem with a Quadruped, where Parts of the Animation were completely broken: the Head had a wrong position while the ears were in the right position.
Apparently the Parent Child structure of the Deformation Bones is not suited for baking and does not always work correctly outside of Blender.
I solved this with the ORG Bones (Bottom Last ...
For the scene global coordinate system, multiply by the object's world matrix:
myObj = bpy.data.objects['testObj']
myObj.location = mathutils.Vector((1,3,5))
print (myObj.matrix_world @ myObj.data.vertices.co) # <----
It sounds to me like you are going to have to repose the object that you are lining it up to. 2.81 Has the new pose move tool in sculpt mode that will make that easy if it is not rigged. However, if you want to pay for something like Auto rig pro, you could have that pose fixed in not much more than a minute the easy way.