To understand this you need to dive a bit deeper into the wood style cloning technique
A clone that is created by using chakra to alter the user's own cells into vegetation. The clones can be as simple in function as a wooden dummy for use in the Body Replacement Technique or completely mobile and able to perform techniques. They have the ability to travel far from the user and are able to communicate with the original. source
Depending on how complicated you make the wood clone yourself it will even be able to communicate. Yamato also should be able to communicate with his wood clone, although this might be harder for him as he does have some of hashiramas cells. But is not as strong/ chakra rich as him
Because they share the same cells, Yamato is able to track its location, communicate with it over long distances, and absorb any information it has gathered by laying his hand on it. Yamato can also use a seed form variant to this technique that operates in the same way: he is able to track anyone that he plants the seeds on by its response to his chakra. source