Hi!
Sadly we can't see your hierarchy in the video, so I can't say if this is a hierarchical problem or a built in feature that is just set to the wrong setting.
Anyway. This happens when the IK controls follow the Root (obviously). Now if it is a hierarchical problem, it means that your foot and arm controlls are parented under the root instead of under the world control. So parenting the under the world should fix it.
If it is a feature, which is called "hipfollow", its something that a lot of riggers build into their rigs because it is easier to get your walkcycle from static at the world origin to moving around the scene if you have a control other than the world that has control over the IK's as well. In this case you would have a constraint with multiple parents on the group above your IK controls, if that is the case you would just need to find the control that blends between the parents by looking at the incoming connections to the constraint in the Node editor and finding the setting that puts them into world mode instead of hipfollow mode.
Once again, I can't really tell which one of the two it is here. But one of these approaches should get your rig to behave like you want.
I hope it helps!
