May not be looking for anything; it may just be a practice exercise.
Drone research takes place in sparsely populated areas. We have drones in South Mississippi, both air and sea, I believe because it's a relatively sparsely populated air space, but I think most of the precursor to that research and development (at least on the air side) took place in the desert where there is really nobody. I completely believe that there are domestic uses in mind, such as searching for something radioactive, and they are going to want to test those uses in more congested air space at some point. That would maybe provide an explanation for doing it when there is still some visibility, so there would be some additional safety even if the downside is public awareness.
I don't want to put too much into what Trump says since he talks off the cuff to say the least, but him saying that he doesn't understand why they don't tell the public what it is makes it seem more plausible to me that it's something in the nature of military exercises without an imminent threat.