How does Western Union track money flows and ensure funds reach the right destination?

Western Union use its own equivalent of a core banking software (to phrase it simply). Every agent is a node on the WU network and WU keeps track of payments via its ledger positions that each agent (or bank) has with WU. Because there is no credit extended, it is all good-funds till settled model. WU knows precisely where the money is who is being paid, where and when, and how much agent balances are.