Just had the same problem and tried using defined reference systems but did not work.
Finally discovered that you need to tick the following box in the STL output options window.:
'Do not translate STL output data to positive space'
I also had a defined coordinate system selected, but think it should work with the default.
My first guess is that Solidworks would be saving with the origin as the centroid of the exported portion of the model.
Try creating a reference coordinate system in SW and using that when exporting your STLs?
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