If the atlas was scaled up or down from the Spine data or project file, then you'll need to use Import Data
and specify the same scale. You can look at the .atlas.
file, newer versions of the format will have the scale at the top. If you don't know the scale, you'll have to guess until you see everything is the right size (try 0.75, 0.5, 0.33, etc).
What do you mean by the assets that are not rigged? I'm guessing you mean region attachments. When the problem is as described above, you'll see region attachments are the wrong size because they use the image file size. Mesh attachments will appear to be the right size because the images are stretched across the mesh, even though the image file are actually smaller or larger than they should be.