Are the payments you make consideration for a supply made by A to you, within the meaning of paragraph 9-5(a) of the GST Act?
No, the payments you make are consideration for supplies made by A to B, not A to you. You are a third party payer in this arrangement. Paragraph 9-5(a) and section 9-15 do not require the provider of the consideration to also be the recipient of the supply for there to be a supply made for consideration. This is made clear in the wording of subsection 9-15(2).
You are an entity set up to make payments to Entity A. You make payments to Entity A for services they undertake. Entity A's services are provided to a third entity, Entity B, pursuant to contractual arrangements. You are not a party to this particular contract.
A New Tax System (Goods and Services Tax) Act 1999 paragraph 9-5(a) A New Tax System (Goods and Services Tax) Act 1999 section 9-10 A New Tax System (Goods and Services Tax) Act 1999 section 9-15 A New Tax System (Goods and Services Tax) Act 1999 section 195-1