Any secrets to making the tapping on that sound extremely clean, like muting frets somewhere? I can play it normally and it resembles the song but I want to be able to play it perfectly. any tips?
Practice, practice, practice. It might be Steve's pickups too. Doesn't he uses Evolution somethings that are clean and clean? I don't know what i'm talking about.
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Are you using the correct muting technique? Putting your left hand over the fretboard to mute the strings?

If so, you shouldn't be having any problems with unwanted noise.
I use the side palm and palm of my left hand to mute the 4 lower strings, lightly resting my third finger and pinky over the two highest strings leaving my middle and index finger free to tap the required notes.