I have read that mulabandha ,in ayp ,refers ( at least mainly) to a contraction and mild,gentle pulling up of the anal sphincter.Also of relevance is that the muladhara/root region is spoken of as including both the perineum and the anus.
And from what i have read and digested so far in the lessons contraction of the perieum is not explicitly stated. I know siddhasana and the SbP- perineum -to brow adress stimulation of the perineum so contraction is possibly not suggested for this reason.As it gets enough coverage. BUt does anyone contract the perineum gently during SBP or any other practice as well as the anus or on it's own.
I've proabbly been wondering about this a for a few years and i think different yoga systems aim to activate all these zones in our nervous system but their emphases may be different as well as their approaches.