Thanks for the links @jsein, it was an intereseting read about mni “rooms”. There’s never a one and only standard for anything in neuroimaging 
I’m still confused about the Hammersmith atlas though. TPM.nii is 121x145x121 (HS is 157x189x156) so it doesn’t fit either. If I understand correctly, the HS atlas should follow MNI ICBM 152 non-linear IV which is also used in SPM. But alas, the array size is still different from HS. I tried padding the atlas by taking into account the difference in the offset of the affines, which does make them overlap. It seems strange to have to take this extra step though, and I’m probably missing something, but I guess it’s a fair workaround otherwise.