I think the OP might have seen it saying rev stst and therefore thought that where it says knit she needs to purl and where it says purl she needs to knit - rather than just following the patter as it says and waiting for it to come out correctly, with the 'right side' showing for the cable surrounded by a 'wrong side' panel.
Hanglider - but you follow the pattern and knit where it says knit and purl where it says purl its just that the 'wrong' side ends up on the front. I think we're saying the same thing but hope its been explained properly.
Rev st-st is reverse stocking stitch, so you purl all the stitches on the right (public) side and knit all the stitches on the wrong (in)side. So yes, you knit the purls and purl the knits!
You do the cable bit as normal - you should have a pattern for just that bit. So you knit (or purl) up to the cable panel, then do those stitches, then go back to knitting (or purling) til the next cable panel. I'm guessing the repeat on your cable is eight rows long.
On the right side of the garment, the cable bits (the bits that cross) are in knit - but in order to show up they are in purl panels. You should just follow the pattern - and there will be a 'cable panel' pattern explanation separate from the main pattern which just shows what lines 1 - 8 are...
I imagine it will be something like purl 3, knit 8, purl 3... knit 3 purl eight knit 3 four times followed by purl 3, cable 4 forwards knit 4, knit 4 from cable needle, purl 3... then knit 3, purl 8, knit 3....
Then the main pattern will show you where the placement of the cable panels is, and where to do increasing and decreasing.