I haven't watched this lesson yet but I found that it comes with training. You really need to be precise in your picking hand to not hit other strings and your fretting hand has to do a lot of muting too. A combination of both should get you there.
Hope this helps
PS: Syn wraps his fretting-hand's thumb around the neck to mute the lower strings when he taps. You can check live videos of him playing the intro of The Stage for an example, but this is only achievable if you have really big hands and or long fingers lol