According to the New England Journal of Medicine article, those white blood cells are still targeting and killing the B-cells. From my (non-biologist) reading of the article, they crafted a virus which targeted all B-cell, of which, some were lukemia. Apparently there are treatments to restore B-cells in a person, so the article seemed to imply once the T-cell count (the "serial killer" white blood cells) went down, they would treat him to restore his normal B-cell count.
Like you, I'm unclear on what exactly the side-effects are here. If they boost the B-cell count in the patient, do they risk re-introducing lukemia? Are these "serial killer" white blood cells a general immunosupressant? There was a part of the article about a developed resistance in the B-cells that I didn't understand.
Either way pretty amazing, and it sounds like while the patient had the worst flu of his life for five days, it's way better than chemo