1. Can you provide the NIfTI image you are using as your overlay?
2. Can you describe what "other programs" you are using?

I think if you use SPM's Check Reg to look at this overlay, you will see that it is not aligned to the background image. I think the "other programs" you are using are ignoring the NIfTI S-form. Seeing the images will test this hypothesis.

The one challenge with NIfTI is that it has two spatial transforms (the S-Form and the Q-Form). In situations where they both exist and where they conflict different tools behavior differently. SPM, FSLEyes, MRIcroGL, etc give precedence to the S-Form (which makes sense, as it has more degrees of freedom so is better for handling registrations). On the other hand, ITK based tools (Slicer, ANTS, etc) give precedence to the Q-Form. This means that images that appear aligned with SPM may have a poor starting estimate for ANTS. For this reason, if you have multiple tools, it is worth setting these to the same spatial transform (recognizing that the Q-Form can not store shear transforms).