I am assuming that these addresses are all owned by Kukoin and if someone is telling me that they own one of these addresses is lying to me. correct?
Correct. I am very certain that it is a scam attempt directed at you.
can I ask him to transfer worth of few dollars to my wallet to prove ownership?
The way to prove ownership of an address is to use a signed message. In that way, it won't requires to transfer fund to establish ownership, but by simply creating a message which signed by the address itself.
I don't know what kind of transaction you are going to conduct, but since you give incomplete information, just be wary of a scam attempt