Tully was born in Mortlake, Surrey, England, to Minnie (née Merrifield) and Walter Edgar Hearman.

Tully boarded at Presbyterian Ladies' College, Perth, before going on to the University of Western Australia, where she completed a Bachelor of Science degree in 1932.

However, her time there was short-lived, as in 1938 she went to Griffith, New South Wales, to work as a plant physiologist for the federal government's Council for Scientific and Industrial Research (CSIR).

For a short period, she was seconded to the federal Department of Agriculture, working on the Murrumbidgee Irrigation Area (MIA).

In 1957, Tully was seconded to the Department of Psychology at the University of Melbourne, conducting research into farmers' decision making with Oscar Oeser and Fred Emery.