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URL = /orderslist?showmaster=customers&fk_customer_id=1

//Server Event
//On Page Load

var_dump($this->getCurrentMasterTable());

Result = "customers" // Success!

var_dump($this->getCurrentDetailTable());

Result = "" // FAIL, empty string, I'm expecting "orders"

How do I get getCurrentDetailTable() to work correctly?

You should not call getCurrentDetailTable() method from Detail table. You should call it from Master table when it is displaying Master/Detail List page.