Check out Justin Sandercoe's lesson:
https://www.justinguitar.com/en/FO-1...mersFlicks.php
Justin uses the term "flick-off" instead of pull-off, because he flicks his fretting finger off the string, so it is a little pluck of the string, which is achieved with a quick downward movement (not a vertical lift).
My pull-offs improved when I started using Justin's technique. Prior to that I was only employing a vertical lift, and it had no power, resulting in weak sound.
However, the amount of "flick" that you need to put into the pull-off depends on how loud the note needs to be, and how much the previous note has already died out, so sometimes you need to flick hard, and sometimes you can actually get away with zero flick (just a vertical lift) , and most of the time it is something in between.
I think I noticed in Justin's lesson that a couple of times he accidentally contacted, with his flicking finger, the string below the string he was flicking off of, so it does seem really tricky, and I would think the usual "mute everything you don't need just in case" rule comes into play, and also maybe the safeguard of making sure the string that might suffer accidental contact is fretting a note in the current chord.