Hello majou,
Most likely the post processing or viewing application that you are using doesn't support large coordinate values - in most projected coordinate system X and Y coordinates are measured in hundreds of thousands or even millions of meters (or feet). If the external application is using 8-bit float type to save the coordinates of the mesh vertices, the decimal digits and some lower order digits will be truncated, which will result in the observed issue.
So you either should use Local Coordinates, which keeps the orientation and scale, but not absolute location of the model. Or use Shift values for X and Y to export the model with the fixed XY offset, compared to the original location.