overlay issue

We collaborate with a scientist from NIH; He uses adobe Photoshop to manipulate and provide images to us. They are "*.tiffs". We upload to ArcPro and conduct our analyses then send analyzed images back. For some reason, our exports do not overlay—they are just off—back on the original images in Adobe Photoshop. We import rasters, we have to convert to vector and we have to add a coordinate system; this overlay issues has been giving us fits.

Any idea will be appreciated!