that tutorial is very outdated and I was very rusty with pivot when I put it together. The next few are a bit more recent. Understand that my animation philosophy is subject to change as I grow and improve, but I stand by what I have taught in the past, and if I change my mind on that I would seek to have it removed. I will perhaps update the animations in some tuts to showcase a higher standard of quality possible through my tutorials teachings. anyways:

The Animation. (yeah its kinda shitty, not my best work but i did this in pivot 3 at school)
I'll begin this tutorial by thanking you for reading! I'm glad people are still interested to learn realistic acrobatics. This tutorial can apply to much more than just tumbling and tricking, however. Double Flips are frequently included in pivot animations for style and giving power to fights. Most often, they're done very "cheaply" because doing them realistically can be quite confusing. Double flips don't have the same physics and properties as single flips, and can't be treated as such. I've color coded this tutorial so it's hopefully quite easy to understand. If you need any extra help, I can be reached on skype: isaacpreston is my skype username

Ref. 1
POSES
I've used red lines to highlight the key poses of this animation. The first one is the beginning of the hurdle into the roundoff, the more drastic the angle, the faster the character is moving. adequate speed for a solid double backflip as pictured should see you at not quite a 45 degree angle on the torso/back leg in this pose. His arms should be up, by his ears, and his front leg tucked in and elevated.
The second pose is the end of the lagstep. notice his chest gradually comes down, even when his legs are moving forwards, he should not lean back here. his torso should be leaned further forward than it was in the first pose.
The Third pose is the top of the roundoff. He is upside down, both hands on the ground. his legs should be coming togetherm and preparing for the snapdown. from this point until the point where he is tucking to flip, his knees should not bend. only his hips. (note- this is unless he is not running very fast into his double back, in this case, a bent knee jump will be needed since blocking will not be powerful enough)
The fourth pose is the key blocking/jumping pose. his arms are thrown up, his legs straigt, and heels off the ground. much like the beginning of the hurdle into the roundoff, the angle of this will be more drastic the faster he goes. a very slow roundoff will have him closer to vertical, and a very fast one will have him closer to horizontal, but shoot him much higher.
The Fifth pose is something most people on DD still cannot seem to make properly. the knees are bent at around a 90 degree angle and the majority of the bend is in the hips. KEEP THE TORSO RELATIVELY STRAIGHT. Tucks look bad with really strongly bent knees and torsos, but very open hips.
The 6th pose is the last essential pose. after the landing, what you do is up to you. The pose should essentially be the tuck pose, but with the arms a bit further up, and the legs straightened, pointing to where they will be landing. This is called "Piking." and is the way most double flips are landed. unless from a REALLY powerful setup, double backs won't be landed perfectly standing.
ANGLES/POSITIONS
First, there is the back leg in the lag step circled. remember, the character steps twice off that foot. once beginning the hurdle, and then once more before transitioning onto the other foot which he kicks off of into the roundoff. Once this foot pushes off the ground the first time, immediately have the upper leg move foreward again, otherwise the lagstep will take too long and have a bad position.
Next there are the 2 blocking frames. These 2 are the only 2 frames after the roundoff in which the characters feet touch the ground. make sure there's always at least 2 frames after the roundoff (not more than 4 or 5 for a super slow one) where the feet are on the ground. this way it doesnt look like he doesnt touch the ground. they are in the same place, do not separate them.
SPOTTING
There are 2 instances of spotting in this animation. Pivot sticks don't have eyes, but the position of the head is an indication of what he's spotting. First the head stays up, with the neck bent in towards the chest, as he sets. Most people whip the head back when he tucks in a single flip, but in a double, I don't advise that, since doesn't spot the ground as soon. This brings me to:
The second instance of spotting, where he sees the ground. I typically advise letting out of the tuck pose when the character is perpendicular to the ground for single flips, but for double flips, the speed of rotation is much faster, so the character will need to let go earlier, but still land low, which is tricky, hence the pike pose. The character spots where his legs will plant on the ground, as his head begins to come back up, only to dip again once contact with the ground shakes him.
SETTING
Notice the arms windmill, it's much more powerful looking than a simple upwards set with arms that stay up until the knees come in. A double tucked backflip looks more conving with all the power you can show, so it's much better to windmill. Remember, when the hands are behind the torso, shorten the arms by about half the lentgh, since most people can't bend their arms straight back.

Ref. 2
Now, we'll discuss rotation. People frequently have issues evening out the spacing in double flips rotations, so to make it easy on themselves, they do stuff like overtucking the character (making him so small it basically looks like a head with one protruding reference to convey his spin) or just make a downright unevenly spaced double tuck. I'm not saying my technique for keeping track of it is the best one, but it definitely helps me.
First off, a rotation that takes place completely in the tucked position should last about 7-9 frames. Remember this.
Also remember, the center of rotation is not the hips. the hips protrude just as much as the head or feet, and you definitely wouldn't center your rotation there (do you???) (THE ANSWER IS NO). I've highlighted the position of the hips with orange dots in this reference, so you can see the general position of them throughout the flip. they push out when he jumps, back in as he tucks, and then up, following the knees that are tucking.
The speed of the knees coming up to the tuck is the most important part, since this determines the speed of rotation, more extreme spacing when the character goes from the blocking pose to the tucking pose means for a faster rotation. The way to judge, is to move the knees up as soon as his feet leave the ground, and then for the entire first rotation, move the knees and feet the same distance in every frame. He should not begin to fall until the end of the first rotation, which is why you can judge this way.
The second rotation is where it gets tricky. Because the movement of the actual character is much more drastic, and downward, it's difficult to keep track of how far to rotate the character. The way to work with this is to stop the character moving once he reaches the top of the jump, and animate the remaining frames of the double tuck in place. (you will quite easily be able to keep track of the spacing, he's still, just remember- 7-9 frames) after you've animated them in place, simply move them into position by editing the frames.
In order to make sure the rotation is evenly spaced after you've already animated the movement (and for some reason it looks wrong, this happens often.) is to export a .gif and import it into flash. draw a box and size it to fit the character on his first frame of his fully tucked pose. make his head fill one corner and his feet fill the one directly below the head. follow the character through the flip, moving and rotating the square to cover him every frame, stopping once he exits his tuck. then, go back through all the frames, and center the square. pick a corner, and draw a dot following it in its rotation. the dot should take between 7-9 frames to overlap its original position, and not increase or decrease space as it goes. You can tell which frame the error is on this way, because the square will have too much or too little space between that frame and the one before it. If there are no errors, and the flip still looks wrong, then the error is in the positions, and not the rotation.
Once again thank you for reading, and if you'd like any additional help, feel free to skype me. I hope this tutorial has been informational and helps people animate double tucked flips better.