What you're describing doesn't sound correct to me. PayPal Payments Standard does display a link back to your store, but it isn't required for a customer to click it for any processing to happen for the payment on the Drupal side. Additionally, PayPal really doesn't do much to encourage a customer to click that link - I'd be at least half of customers won't be coming back by your shop after submitting payment unless they're different than mine. : )
What sounds fishy, though, is that your orders remain in "Checkout: Complete". Technically, they should be remaining in "Checkout: Payment", because that's the status they're in when the user redirects to PayPal. However, the IPN must be coming through and triggering some order status change, which is followed by the IPN listener simulating moving the order to the next page, "Checkout: Complete." You need to look into what rules you have operating on when a payment is received in full for an order, because the IPN triggers that whether the customers comes back to the site or not. You are probably changing an order status and it is getting set back somehow.