can the code-generating software (AdminApp) be setup to be triggered automatically?

No, the way that e-commerce automation is handled is by per-generating a block of codes and using these as “stock” – each time an order is received the next un-issued  code for that title is sent to the user, either manually or automatically, typically as part of an email. The automation can be achieved in one of three ways: (i) using a commercial service, such as getdpd.com or others like this; (ii) using third party low cost code, such as that from Vibralogix; or (iii) generating your own code, e.g. in php. to pick codes from lists that are stored on your server.