It sounds very much like the customer is not clicking to return back to Shopify. When an Order is placed through an external gateway like PayDollar, the customer enters our cart, moves to PayDollar to put in their details, then clicks to send the payment. Once they've completed the payment, there will be an option to return back to Shopify (usually "complete checkout" or something similar).
Shopify won't make an Order until that link or button is pushed, because we need an API signal from PayDollar to know that the checkout is over.
It helps to remind customers in the cart to tap that button at the end of the transaction, and let them know this will make sure they get a receipt with the full details of their order. :)