As indicated in my previous post, the arming/disarming (exit/entry) delays are controlled by the SmartApps and not by the device handler. Depending on the SmartApp you’re using you can configure it to have separate delays for different arming/disarming modes.
For example if you’re using Intruder Alert with Alarms, you may want to install two instances of the app, one for Armed away and one for the Armed stay (set in the Arming conditions page for each instance). Now for each instance of the app you can configure a separate Exit delay (arming delay). When the instance is activated (based on what’s set in the Arming conditions page), it will send the configured delay (or not) to the Ring keypad (via the device handler).
Regarding WebCoRE, there was a typo in the first post, sorry about that. You would need to subscribe to the attribute armMode for your keypad and the value of the attribute will tell you what mode it’s arming/disarming (rectified the description in the first post).