This might be my own stupidity, but I wasn't able to get the backside ring to stick. My kick drum reso has a dampening ring. I cut the hole so that the edge of the hole is right next to the edge of the dampening ring. When I went to install this O-ring, the part that's supposed to go on the inside of the kick didn't go in place no matter how hard I tried. Because it didn't go where it should have, it remained kind of halfway installed, which in return resulted in a very noticeable buzzing or rattling sound.
Can't be sure if I just messed up or if the ring in question was faulty, but results were not great in any case. However, it seems that you can get away with just the outside ring in place. At least it hasn't fallen of in the month that I've had it.