If by moving the rig itself you mean using something like MoveTo(), that’s generally what you should do. If by tweening it in a script you mean tweening the CFrame of the HumanoidRootPart, that’s not at all how you should do it. Tell me if it works for you!
Sorry for my wording what I meant by moving the rig itself is that I would move it in the animation editor itself. If your opinion changes please let me know!