Those two-pronged rivets are called harness spots and they do need to reach all the way through the leather and bend to be secured fully – just like brads.
Setting spots is pretty similar to setting snaps. You want to use a maul or wooden/poly mallet. You need a hard surface, but in this case, you’ll want to make sure you that you are using some metal to reinforce your spot so that the tails bend back securely. For that, you can use the nifty metal piece that comes in our spot setting kit along with poundo/poly board and marble/granite or just use a piece of steel (or other hard metal), like Denny. No matter what you use, keep in mind that it needs to be very hard so that it will bend the tails of your spot. It may take you a few tries to get the proper hang of things, so be sure to test setting a spot on some scrap leather first.
Your setter definitely needs to match your spot size since you’ll be placing the spot inside the setter. Last, you’ll have to put some power behind your mallet or maul. Due to the rounded nature of the setter, giving your spot a few extra taps should not distort its shape.
Here you’ll find a very roughly cut video of Denny demonstrating setting spots. You’ll notice that even a master craftsman has a tough time getting things right every time, but you can always start things anew.