Fall under your umbrella

Does anyone know the original meaning to "Fall under your umbrella" as in "That should fall under your umbrella."

Umbrella in this sense means jurisdiction or responsibility. For example in a supermarket the purveyance of vegetables might fall under the umbrella of the produce manager.

www.m-w.com gives the following definition for this sense: "4 : something which covers or embraces a broad range of elements or factors "