They didn’t.
You opened the pay online application yourself. All it did was go back and look for payments you had made in the past and proactively copied the reference numbers and biller ident, and then made a list of them.
These reference numbers and biller ids are the key, assuming it works much as it does where live. The billing mechanism takes your payment and uses it to access a common billing clearance system. That system is keyed by the biller’s ident. The biller’s ident isn’t a bank account and the payment isn’t a direct transfer. If the bill was previously paid by the teller using this system they already have everything needed to know the previous transactions were bill payments and what both your reference number and the biller’s ident are.
Had you paid by a direct bank transfer of funds the bank would not have been able to see the transaction as a bill payment, but that won’t be how it happened.