Most likely you would be using our Integration feature to have the order data sent to your fulfillment house after payment is completed, either as an email or as a Web-based POST submission:
http://www.e-junkie.com/ej/help.integration.htm
In a nutshell, if they can already accept PayPal IPNs, they should be able to accept our Integration submission which follows the IPN format; they would need to be able to handle or ignore some extra fields we may add to the submission, and should have some way to disable validating our "IPN" with PayPal, which would fail since we are not PayPal (and we already validate the original IPN with PayPal ourselves before we forward the data anyway).