Manual position interpolation like Rigidbody

My current situation is as follows:

I’m currently controlling an object within FixedUpdate() but without any physics (no Rigidbody and so on).

Now, of course, the camera shakes since it’s using LateUpdate(). Controlling the camera with FixedUpdate() of course works but I can’t be sure that it’s updated after the targeting moving object so it may sometimes have a wrong position since the moving object hasn’t moved yet.

How does a Rigidbody do it’s interpolation? Is it a simple lerp of it’s position in Update() or something like that?

If you’re animating kinematically, then you don’t need to worry about rigidbodies at all. You probably just need to handle the movement in the Update function (not FixedUpdate), but scale it by the value of Time.deltaTime (this is the time taken for the last frame to render). This way, you make motion time-dependent rather than moving a fixed amount per frame.