I went digging through that controller and software and it appears it doesn't offer the "normal" access control options I'd be used to however for clarification:
A REX pir or via handleset/crashbar, will typically allow the system to shunt the DSM for a programmable period of time. This would prevent door prop (held too long) or force (opened without credential, IE: key) and would identify trouble points before they became problems, usually it's an end user that causes those events. In the case of most PIR based REX's, they typically would unlock and shunt a door contact at the same time (bypassing a forced door notification) and keep an end-user from crashing into a locked door, so the doors would unlock as they approach from within the protected area, assuming no "push to exit" buttons are being installed. Also, by installing a REX, you'd be able to parallel any variety of NO circuit devices to provide an unlocked action in addition to bypassing any DSM. If done wisely, you'd be able to trigger a generic input anywhere on the system to provide an output anywhere else on the system without the need for more wiring. Infinias doesn't appear to be a 1:1 I/O unit, so mapping appears to be possible.
A door prop or force would either cause an event to fire on the host workstation (only useful if monitored by security) or could be mapped to an output, such as drive an alarm panel for monitored security purposes. In the case of a panel like an Elk, you could map the ACS output to the M1's input to automatically disarm when the first ACS user comes in, then set an auto-arm for a time or if the last out forgets to arm the system. Instead of installing a bunch of door contacts, you would just install DPDT units in the doors and split the circuits between the systems.
We generally use Viking units for our telephone release and interface to client phone systems, however if your system provides a momentary dry contact option, it appears like you'd be able to map certain items across the software and network to your door controllers rather than pulling cabling everywhere.