Someone asked about this on Stack Exchange: https://chemistry.stackexchange.com/questions/84704/how-can-...
They never got an answer.
To be clear, the container wasn't disturbed or vibrated excessively. The liquid was never spilled outside the container. In my case, there were 3 plastic cups in a single tray, all connected, and the substance grew out of one cup, down into the bottom of the next cup over, and then started back up the other side of the empty cup which had never had liquid in it. This isn't a residue left over by evaporating liquid. A thin film of this substance grows on surfaces above the highest point the liquid ever reached. Clusters of the stuff started forming a couple inches from the only container that ever contained liquid.
I asked about this just today on Reddit actually: https://www.reddit.com/gallery/u85pwz