Ecobee integration does not support rule based automation, no. Supported features are listed in the link above. Z-wave thermostats have the most functionality and integrations as they are directly connected to and controlled through the alarm panel.
Those emails are generated by ADC. Can you forward that email to firstname.lastname@example.org so I can reference it to Alarm.com and have them remove non-applicable details for thermostats that do not support them.