Cool lesson.
I'll admit that it took me several years to develop a good vibrato. It's not something you really pay much attention to early on and is a very overlooked technique. It usually just comes with lots of practice. Some players never develop a good vibrato.
It's all in the wrist for me, and playing lots of Dimebag riffs and solos. My playing developed quickly when I started learning Pantera songs cause Dime had the perfect technique and such a sweet vibrato.