The whitepaper (and some of the links to the wiki) mention the transaction manager as a key component. In the whitepaper, there’s even a Step 4 in the transaction process going from the transaction manager to the receiver saying ‘Notify the transaction’ (which would seem to answer my original question).
However, transaction managers are being / have been removed, so this diagram does not answer my question.
These changes resulted in the Unified Structured Data RFC link from the original post, which is what led to my confusion about notification of payment.
So, still not clear, but thanks for the replies so far.