It is not required in tamattu' that the two pilgrimages be for one person
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Is one considered to be performing tamattu' if he intends the 'Umrah for one person and the Hajj for another?
Yes.
He is considered to be performing tamattu'. The scholars (may Allah have mercy on them) stated explicitly that it is not required in tamattu' that the two pilgrimages be for one person. Rather, it is permissible for the 'Umrah to be for one person and the Hajj for another, or for the 'Umrah to be for himself and the Hajj for another, or for the 'Umrah to be for another and the Hajj for himself. They consider all of this permissible, and it does not invalidate the tamattu'.
Yes.
He is considered to be performing tamattu'. The scholars (may Allah have mercy on them) stated explicitly that it is not required in tamattu' that the two pilgrimages be for one person. Rather, it is permissible for the 'Umrah to be for one person and the Hajj for another, or for the 'Umrah to be for himself and the Hajj for another, or for the 'Umrah to be for another and the Hajj for himself. They consider all of this permissible, and it does not invalidate the tamattu'.