Well, when you thump perpendicular-wise, you can still bring your thumb underneath the string like you do in the perpendicular way. But don't plan on actually having your thumb directly under the string after the thump -- that'd be pretty difficult to do and manage to have the string ring afterwards instead of muting it. What you do is only move your thumb down just a bit, but more to the side (towards your chest). Then take your thumb and pop it back up, using the tip of your thumb.
It's a pretty great technique -- double thumping. I don't really use it these days because of that thumb/pinky thing. I also am able to generate a fast double thump sound by simply rapidly slapping the string twice consecutively. So what'd probably be more useful for you to learn is the "triple-thump" -- adding an index finger pop after the double-thump to form a fast triplet.
Just mess around with it and find what works for you best -- sounds the coolest, and is the most relaxed.
