Okay, so.... weird bug:
I made a mod that makes buildings take a while to be "built" and until they are fully built, they are disabled and not operable. If I do that with mining depots and then re-enable them and make them operable again when they're fully built, and I put the mining drones in, they are instantly completely full with the selected ore.
Any idea why that is happening and how I can prevent it? Right now, I just ignore mining depots and leave them alone, but that is a lazy work-a-round.