Some people think that because the drone is in the car, it will maintain its position. But just think of the sensation you feel in your eyeballs or guys when accelerating in a fast car. There's a bit of inertia there too, right? The same thing is happening here. All the air gets "pulled" to the back of the car (we know it's trying to stay still in relation to the earth).
The object in motion will always try to stay in motion, which means that when the car is traveling at a constant speed, the drone will stay still as well. It's the same with us human beings, which are stationary in relation to the planet we're on, but moving at high speed through the universe.
The helium balloon experiment is another fun piece of science. The air still rushes to the back of the car, but since this reduces density at the front, the balloon tries to "lift" itself in that direction.
On a side note, this is probably the only experiment where a cheap drone and a balloon are more useful than a $1000 DJI model. The sensors are trying to stop it from crashing into the back of the car, thus making it inposible to test.