It seems to me that the wobble developed in the base and was carried upwards with pulling the walls up. You were good after centering and pulling out to get the clay ready for wall pulls. it looked to me like the first pull was good, and when collaring some unevenness of the walls may have crept in. Around 3:20 it starts to be noticeable and from there becomes more noticeable as the video progresses. As you continue to expand the form the issue becomes more and more noticeable. Once this develops it is hard to correct as the form starts to push the clay into more unevenness due to the wobbling.
The continued use of water reduces the strength of the clay, and it would benefit you to learn to use the slip from centering for lubrication instead of more water as you pull the walls up.
I recommend getting all of the height of the cylinder before starting to form the walls. As you gain the height, slow the wheel down progressively. Clean off the slip before you start to change the shape. Once you start to change the shape, very slowly make changes from the vertical profile. The clay consists of platelets that need time to move over and around each other, and making small changes helps this process. Getting too greedy with pulls or shape changes leads to problems.
You have done a pretty good job of self training from videos. Now the nuances need to be addressed. Ask more questions, as this forum is a helpful bunch. Good luck with your progression of skill.