Livebearers will breed as soon as they see each other! The lady in the LFS is clearly a fool! However, all is not lost. There's no problem if they do breed, you don't really have to do anything special (it's not like when cows give birth...!).
If you want to keep the all of the fry, then you'll need to separate them from the adults (there are various ways of doing this), but I'd suggest that your best bet is just to leave them to it. I did this when I used to have livebearers - they breed, give birth, almost all of the fry get eaten (not very nice for them, but entirely natural, and the fish that eat them will be happy), and you get to watch a few cute little babies develop. If you want to give them a fighting chance then you'll need a few caves with small openings that the fry can get in, but the adults can't.