The use of the word "Steeping" is completely inaccurate and improper, but is recognized in vaping nomenclature. Aging or curing would actually be the most accurate descriptor of the process. To understand the science one need to understand the process and methods involved in making e-liquid.
Concentrated flavorings used in making e-liquid are specifically made for the food and beverage industries. Most of their processes include heating, carbonation, or dilution which aid in the curing or flavoring process. Nicotine for example has a peppery taste to it which can be detected in fresh e-juices which when aged or "steeped" become less detectable.
By shaking the bottle vigorously it creates bubbles and micro-bubbles. Removing the dropper and cap allows the nicotine and flavorings to outgas while exposing the e-juice to oxygen. As for the science behind it....ya...there is about 2,350 years worth. So why are there some juices that do not require steeping? Some juice makers employ different processes such as heating which speed up the aging process. This is why custom juice makers that do not employ such speed-curing processes note that their juices require steeping for the flavors to reach full maturity.