Thanks for input Joe,we'll be waiting for this lesson!
Inertia,your issue is mostly related with routine
which comes with lot of practicing.
I haven't thought a lot about it when I was practicing tapping
for the first time,I was just trying to find a way to keep it clean.
And here's what I do know now.
You mention anchoring tapping hand on the fretboard.
Yes,that would be one way to do it but that limits you
to only one or two strings to tap,usually higher strings
cause you will anchor your tapping hand on lower strings.
Second way is to be VERY careful with power you're
using when you tap,too much power in tap
will force some open strings to ring.
Third way is to mute all unused strings as much as possible.
And that is usually done with your left/fretting hand.
Per example if you're playing some tapping on D string,
you should use your left hand index finger to do 90% of muting.
Just lay it easily on G,B and high E string,enough to mute them a little
but not too hard to fret them.
Also,tip of your index finger might touch A string as well do mute it.
Forth and also very important way is to tap ONLY
the string you wanna tap,avoid to touch strings around it.
If your action of the strings is too high it might be difficult
not to touch some neighbor stings so check your action as well!
Finaly,combining all these 4 ways/methods you'll be able
to play tapping nicely and without any noise.
So my advice is to look deep into your tapping playing
and locate what you're missing from these 4 ways/methods,
then simply apply one of few of them and see the result.
Hope this helps a little.