The headers must be the same. All the processing is done in native T1 space.
Hence all the intermediate and final output files should have the same header as the T1 image. If this is not the case, then the processing resulted in wrong outputs somewhere.
We never observed this mis-match in my evaluations -- and nothing of that sorts was reported earlier on this forum. However, I am mentioning this because, this is the only way the images will rotate -- and you mentioned that such rotation pblm did occur in your case.