Address change confusion
No, they would not. In Bitcoin, wallet is an abstract concept as it is just a software that manages your private keys and addresses. The addresses generated from the private key in your wallet bear no resemblance to others. Unless you explicitly mention it to them that it is your address, there is no way of knowing whether it is you who has sent the bitcoins to your client. From their perspective it might be as they received a 'donation' of bitcoins from some random person.