I think there may be a confusion about the solution in the way you approaching the problem. We substitute protons with other atoms (you use Cl) to produce our stereocenters in case they are not already present. Here, we have stereocenters for both our protons already so we can go about determining their relationship by mirror-imagining our molecule.
I do get (S,S) for the given molecule, however upon mirror imaging it it becomes (R,R). Therefore, the two protons are related enantiomerically and thus enantiotopic, as opposed to diastereotopic in which (S,S) and (R,S) would be so. I hope this makes sense.
EDIT: As a side note, the protons would only be homotopic if the compound was a meso-compound (see attached).