A bank will typically require correspondent accounts for holding currencies outside of jurisdictions where it has a branch or affiliate.
With few exceptions, the actual funds held in any foreign currency account (whether for a bank or for its customer) are held in the bank's correspondent account in that currency's home country.
Even where a bank has branches or affiliates in multiple jurisdictions, balances in a foreign currency account in one jurisdiction are held with a correspondent account at either that bank's branch or affiliate in the foreign country, or at another institution.
A Dutch oil company is a customer of ING in Amsterdam, and sells a cargo of 500,000 barrels of oil for $40 million to a Swiss trading company who is a customer of Credit Suisse.
ING Amsterdam holds its dollars at Bank of America (BofA) and Credit Suisse holds its dollars at The Bank of New York Mellon (BNY).