I don't know, but I can think of a few possibilities:
1. The amount demanded varies from incident to incident. Bitcoin is fractional to 8 decimal places, so it's possible to narrow down the list of victims by the last N digits of the payment.
2. The original demand for payment includes instructions to list the address you sent from. This would be a lame solution for many reasons, including (1) these victims are probably all new to Bitcoin and would have no idea what an address is, and (2) according to an article I read, some security consultants keep a Bitcoin wallet handy to pay on behalf of their clients, leading to duplicate payer addresses.
3. Same as #2 but demanding that the victim include the transaction ID, which is a long hex string. Similar usability issues.
4. It's possible to embed metadata into Bitcoin transactions. As with the prior approaches, victims would likely get this wrong.
Most likely there's a human criminal on the other end of the exchange, and that human matches up victims and payments.
Because the paying victims are surely unsophisticated about Bitcoin and terrified about what is happening to them, it seems likely that the risk of one victim claiming another victim's payment is small, so the manual match-up method is probably the most practical solution from the criminals' standpoint.