A relative does Qur'baani for us. However, we pay him for the animals only after the Qur'baani has been made.

Answer

When the price is not specified, there is jahaalat (ambiguity) in the sale. There are two types of jahaalat regarding sale transactions. Such jahaalat, the consequence of which is dispute (mufdhi ilat tanaazu'), and jahaalat which does not lead to dispute.

In the first type of jahaalat which leads to dispute, the sale is faasid (corrupt), and it is Waajib to cancel it. If the jahaalat does not lead to any dispute, then the sale will not be faasid.

Assuming that the jahaalat in the transactions arranged with your relative does lead to dispute, then obviously the sale will be bay' faasid, cancelling of which is Waajib. Failing to cancel it is sinful.

In the scenario you are in, even if the sale is faasid the question of cancellation does not arise since the animals have already been sacrificed. The question now is: Is the Qur'baani valid?

When the sale is faasid, the buyer becomes the owner of the asset when he takes possession of it. Thus, the animal purchased by way of bay' faasid became the property of the buyer when he either physically took possession of it, or allowed his Qur'baani to be made. Since he made Qur'baani of an animal which is his property, the Qur'baani is valid. But he has to make Taubah for the haraam act of entering into a faasid transaction and abstaining from cancelling the sale.