It was indeed because the watermark image uses alphablending, the insert method used imagecopymerge() does not support that, so you lost it when the watermark was copied in.
In a loop, foreach images, I copy the image : File::copy(...), then I do a rotate : Image::load($file)->config('bgcolor', null)->rotate(90)->save($file);
I don't have Photoshop (no Windows), but I've tested in two image viewers, in Firefox, and GIMP. If I remove the alpha channel of those images in GIMP, I get a white background.