You are absolutely correct. Take a look at the “Guide for EZIOxx Set-up and Configuration Utility” in the downloads section for the EZIO8SA. You will see a section in that PDF (page 5) where you can program the module to issue a command going from off to on and a different one for on to off. So, for turning on, you can have a command sequence of 00 00 (which would do nothing), and then a turn off command to the group when the input goes off.
Feel free to download the utility (free download) and it will give you a good idea of what you can do.