You're supposed apply pressure onto the bottom of the deck to keep it from falling apart. You should be pressing down really hard with two of your fingers. For me, the pressure points are the top pad of my thumb and the top knuckle of my middle finger.
You also want to look at how you go from faro to fan. For me, it's much easier to actually reposition the deck. After you faro the cards, try moving them around without spreading them, holding only the bottom end of one side. Get a feel for things, and how much pressure is require to keep the cards intact.
Remember that giant fans don't work the same as a thumb fan. You don't even need to touch the sides of the deck with your fanning hand. The only card I touch when I fan is the top card, all the way on the edge, and I get perfect buttery fans every time.
Also, practice. Seriously, it doesn't matter if you fail 99/100x. Eventually it'll be 98/100, then 9/10, 5/10, and one day 0/10.