From time to time, Quiet will call a supply drop for you. It seems to be identical to the one called from your iDroid.
What are the requirements for Quiet to call a supply drop for you?
Reference: Official guide book, page 302: Retrieve a supply drop ordered by Quiet (up to five times per mission/free-roaming sequence) +0.5 bound. On page 305 (same book), you get a table called Quiet's Supply Drops which tells you what she gives you depending on your bound — there are four tiers. However, there are no indications as to why or when she does order a drop. You have to keep your eyes open. I am assuming it is when one of your items runs out.
Best Answer
In my experience, when Quiet scouts an outpost, she will gather supplies whilst moving through the area, and then leave said supplies at or near one of her vantage points.
These supplies are not being dropped in from the sky.