You are both in contract when both Parties start acting as if you are in contract: the problem comes if the written draft contract has been going back & forth between the Parties and it is unclear when both Parties starting acting as if they were in contract and hence which 'draft' is actually the contract.
So if you respond and authorise the payment, you would definitely be in contract, but you may well have done actions before this and hence be in contract.
So if you respond and authorise the payment, you would definitely be in contract, but you may well have done actions before this and hence be in contract.