I would recommend that you not only follow up with a call that outlines financial responsibility but also what is to be provided.
Further from my experience as a procurement agent, I would follow that phone call with a confirmation, in the form of an email, of your interpretation of the conversation and the agreement of who and what is required by each party.
Trust me on this issue, you need to document everything. If all comes out right, then great and that will most like be 80% or 99% of the cases, but when everything hits the fan, you will be glad you documented everything.
We document, not because of the responsible supplier, but because of the few who are not. Sadly, we only find out who is the responsible supplier and who is the other after the rest hits the fan.