I didn't fasten it to them, with the back seats locked in and the 7/8 dowel rod in the slots it holds firm. If I do happen to have any issues I will probably use a velcro strap to hold it.
Getting the carpet around the corners took some doin, I used a hair dryer to heat the carpet and mold it around the corners. I don't plan on using the shelf for anything heavy. I will put some strap system on the top, I have been looking at battery hold down straps at Tractor supply. All that is, is a 1 3/4 nylon web strap with two plastic brackets that screw to the shelf, then you slide the webbing through and it has a buckle on it. Either that or I drill a series of holes and thread 1/4 bungee cord like lacing a shoe.