If you have the exact same settings (“relative detail” for example) you have to keep your camera at the exact same distance to your model as Kent does in the video.
You can only smooth existing geometry. Try setting your brush-strenght to 0 and click on an area without smoothing to create new geometry without deforming the mesh. Then smooth on that area.
I find this easier with “constant detail”, “collapse edges” and a value around 5%.
I hope I understood the problem and could help 😉