The two main right hand techniques I use are simply options of sound and tone for me. Although i've worked a lot on the "regular" style of finger playing as well as the thumb and finger technique you're asking about, the choice of when to use them is not something that's conscious now.
The muted thumb technique gives me more of a punchy tone, and I end up playing some higher notes with my fingers within the bass line, and that lends itself to being a little more melodic in the line.
I have a ton of exercises for that, and put them all together for a 12 week bass lines and groove course on videobasslessons.tv. There are some free preview videos on my youtube channel if you have a second to check them out. I take a look a bunch of different bass styles starting with video #1 here: https://www.youtube.com/watch?v=x83qXXLWjak