Hasta La Motion!

So its my first time posting and hopefully someone has the answer 🙂

In regards to compositing, either 2 separate videos or with cgi, one thing that has me stuck is when there is some sort of interaction.

What I mean is when something for video 1 interacts with video 2 thats been masked in for example. Say when someone hands someone something. How is it made to look 100% spot on?

If you take a look at this video and go to the shoot from 1:50

you can see how its not perfect but close, but then in the final shot, when he hands him the stick and hat its 100% perfect.

So what is being done it to turn a "almost there" into a perfect fit?