Plum Tree Blooming In October . Even those aren't on all branches. Growing to a height of around 10 feet in full sun, with a spread of about the same, this is a great option for a smaller home garden. Chickasaw Plum Chestnut Hill Nursery from chestnuthilltreefarm.com X cistena) and the “dwarf natal plum” (carissa macrocarpa) which grow to height of 5 to 7 feet. Here in virginia, my best guess is this: How to plant a plum tree.