Praise be to Allah.
The basic principle is that the one who is appointed to do something on behalf of someone else is entrusted with that task, which dictates that he should carry out the task in the manner that is in the best interests of the one who appointed him, and that which is in the best interests of the one who appointed him in this case is that he should do tamattu‘ on his behalf, as this is what would be in his best interests if he was doing Hajj himself.
It was narrated that Anas ibn Maalik said: We set out declaring our intention to do Hajj, then when we came to Makkah, the Messenger of Allah (blessings and peace of Allah be upon him) instructed us to make it ‘umrah [to be followed by Hajj, i.e., tamattu‘]. He said: “If I had known before what I know now, I would have made it ‘umrah, but I have brought the sacrificial animal with me, so I will do Hajj and ‘umrah together (qiraan).”
Narrated by Ahmad (12044); the hadith is also narrated in as-Saheehayn.
So if the one who appointed him or hired him stipulated that he should do a particular type of Hajj, then he must adhere to what the one who appointed him stipulated.
See also the answer to question no. 1745 .
And Allah knows best.