This phase II trial tests the effect of adding ruxolitinib to standard graft versus host disease (GVHD) prevention in treating older patients with myelofibrosis (MF) or myelodysplastic syndrome/myeloproliferative neoplasm (MDS/MPN) overlap syndromes before, during, and after a donor (allogeneic) hematopoietic cell transplant (HCT). Allogeneic HCT is a procedure in which a person receives blood-forming stem cells (cells from which all blood cells develop) from a genetically similar, but not identical donor. Giving chemotherapy, such as cytoxan and busulfan or fludarabine and melphalan, before a donor transplant helps kill cancer cells in the body and helps make room in the patient's bone marrow for new blood-forming cells (stem cells) to grow. However, sometimes the transplanted cells from a donor can attack the body's normal cells (called GVHD). Giving standard prevention (prophylaxis) therapies, such as tacrolimus and methotrexate, after the transplant may stop this from happening. Methotrexate, a type of antifolate, is in a class of medications called antimetabolites. Methotrexate stops cells from using folic acid to make deoxyribonucleic acid and may kill cancer cells. Tacrolimus is used to help reduce the risk of rejection by the body of organ and bone marrow transplants. Ruxolitinib, a type of Janus-associated kinase (JAK) inhibitor, blocks a protein called JAK, which may help keep abnormal blood cells or cancer cells from growing. It may also lower the body's immune response and prevent the development of GVHD. Giving ruxolitinib before, during and after allogeneic HCT in addition to standard GVHD prophylaxis may be safe, tolerable and effective in preventing GVHD and improving outcomes in older patients with MF or MDS/MPN overlap syndrome.