Summary
Slicer loads the image correctly (tested with Slicer-5.2.2 on Windows).
The STL file that you attached is in incorrect location (it seems that it is shifted so that all its point coordinates are positive).
Details
Info from DICOM image header
Rows x Columns: 390 x 390
PixelSpacing: 0.2, 0.2
=> This means that the frame size is: 78mm x 78mm
ImageOrientationPatient: 1, 0, 0, 0, 1, 0
=> This means that slices are axial
ImagePositionPatient for each frame (in LPS):
-39, -39, 30.5
-39, -39, 30.3
-39, -39, 30.1
…
-39, -39, -30.3
=> This means that the image bounds (in LPS) are: [-39 to 39, -39 to 39, -30.3 to 30.5]
Comparison to image and STL file bounds
These bounds are exactly where the Slicer-imported image appears in:
Therefore, Slicer loads the image into correct location, as specified in the DICOM header.
In contrast, the STL file that you included in the zip file is in incorrect location, as its bounds (in LPS) are: [0 to 78, 0 to 78, 0 to 60.8].
What to do?
If you just use Slicer and other software that loads the images and saves segmentations correctly then you don’t need to change anything - just keep using these software.
If you want to use that software that created the STL file in the incorrect location then you may able re-export correctly by either adjusting its STL export settings (disable enforcing of positive point coordinates), or by saving the mesh in a different file format (such as ply or obj).
Note that point coordinates in STL files are forced to positive in some software because 35 years ago in the original STL file specification they specified an arbitrary limitation that coordinates in STL files must be positive. While most software simply ignore this unnecessary limitation, some sofware modifies the mesh during export to ensure that coordinates are all positive. This shift cannot be undone: the original, correct coordinates are permanently and irreversibly lost.