From the original paper:
DHIES is a Diffie-Hellman based scheme that combines a symmetric encryption method, a message authentication code, and a hash function, in addition to number-theoretic operations, in a way which is intended to provide security against chosen ciphertext attacks.
So the MAC is in this case already part of the scheme. If implemented correctly encryption should result in an ephemeral public key, a ciphertext, and a MAC / tag for the ciphertext being generated. So there's no need to generate another MAC.
 The distinction between DHIES and ECIES is simply the type of group being used for the underlying algebra, it isn't important in this context, much like the distinction between DH and ECDH