It works with every character. When you dash, from 4 onwards till the end of the dash (with fox the dash is 22 frames for example) you can (smash) turn (However you can turn immediately from dash done out of turn aka dashback). It functions very similarly to doing turn from wait, the animation looks the same, except it stops your horizontal momentum. However, on the second frame of turn, if you are still holding the analog stick input, the turn is cancelled into dash. This is what enables dash dancing: you just dash -> turn -> cancel the turn into another dash and so forth.
So in order to empty pivot (which was for some reason renamed perfect pivot in sm4sh, heavens know why), you need to press the turn input precisely for 1 frame, which is pretty hard. You can also just do any move except neutral b on the second frame of the turn. Moves take priority over dash, so you can dash -> turn -> c-stick fsmash without having to worry about releasing stick. You can also shield, jump and grab on the 2nd turn frame. If you don't release the stick, you have to do the action you want frame perfectly on the 2nd turn frame because you will dash otherwise.