Is the Hady (sacrificial animal) obligatory upon the deceased (so-and-so) or upon the pilgrim performing Hajj on his behalf, in the event that the pilgrim performs 'Umrah upon arriving in Makkah and then Hajj on behalf of the deceased?

If you volunteered to perform Hajj on behalf of a deceased person, and you were asked to perform Hajj ifrad (single Hajj), but you performed Umrah for yourself and then entered into ihram for Hajj ifrad on behalf of the deceased, then you are liable for a hady (sacrificial animal) and another dam (blood sacrifice) for entering into ihram from Mecca. It is more cautious to return to the miqat (designated point for assuming ihram). The deputy is responsible for the blood sacrifices for errors from his own money, except for the dam of tamattu' (Hajj combined with Umrah) and qiran (Hajj and Umrah performed with a single ihram) if he was given permission for them, in which case they fall upon the one who commissioned him.

If you received funds for performing Hajj ifrad on behalf of the deceased, and you returned to the miqat and entered into ihram from there, then there is nothing upon you. However, if you entered into ihram from Mecca, then you are liable for a dam for neglecting the miqat, and you should refund an equivalent amount from the funds.

If you were instructed to perform tamattu' but performed Hajj ifrad, then you must refund half of the funds. If you were instructed to perform qiran but performed ifrad, then you must refund from the funds an amount equivalent to what you omitted by not performing the ihram for Umrah.