Sounds like your file is too large to share. Character animations might have a lot of elements. So, a general answer might end in a disaster.
Having said that, typically, anything in Cinema 4D relates to the World Origin as the main parent. This means, if you create a Null, with the Origin at zero for position and rotation and one for scale, you should be able to drag everything and this Null and rotate the Null then. Again, at the moment, there is an expression, for example, that operates on Global values, that will not fly.
Create this Null manually, do NOT use the Group short cut; it will typically not land on the World Origin point. A reason why I would love that the Group short cut would be eliminated for good and not spoken at all anymore
If the Null is not at zero (Pos/Rot) and one (scale), the animation might be broken for good. So, do it manually, please.
I hope this will work for you; as you mentioned, Mixamo, import and done, no additional influences.
Set up animation clips, then use the Animation> Pivot Object, which can be set directly in the Animation Clip. The Pivot Object will take over.
If you have just one animation sequence and the figure should move differently, use the Skin Object. In the Skin Object, you can determine which Coordinate system can be used. Skin> Object> Coord.: Object.
This sets the Object Coordinates as the main source for the animation and leaves the joint rig indented from its position.
Try each option with a copy, as I don’t know about the elements of your set up.
All the best