Is it normal to have a mastectomy and radiation therapy afterwards, rather than the other way around?

Yes.: A small subset of patients who opt for or require mastectomy for local treatment of their breast cancer will need radiation therapy; this is always done after surgery. Furthermore, if they require chemotherapy, this too will be given before the radiation therapy.

This can be normal: If a patient has mastectomy and the lesion was large or had many nodes involved this is followed by chemo then radiation. If the patient had a lumpectomy then radiation they would not need mastectomy. However if later on it recurs one can still have a mastectomy. This does not happen often.