Is being premature and having polycythemia related?

Often yes. Premies can become polycythemia for many reasons, often polycythemia is a babies reaction to having poor blood flow or due to maternal diabetes. These conditions can also lead to prematurity. Infants can also become relatively polycythemia from dehydration as this results in a low ratio of fluid to red blood cells.
Dehydration. Premature babies are more likely to be born small for gestational age and dehydrated, therefore polycythemic. The degree of prematurity determines the outcome by far.
If they are multiple. Usually premature babies tend to have less amount of hemoglobin than term infants, even though they have more blood volume for the weight. But because of ttts, the recipient twin tends to be big and polycythemic and the donor tends to be scrawny and pale.