I use push notifications on my iPhone all the time and that is definitely not the intended experience... they should be pretty much real-time.
The first thing I would try to do is to reboot both your Xfinity Wireless Gateway and then your Xfinity Home Touchscreen Controller to make sure they are in good communication with each other.
I would suggest logging in to the Xfinity My Account App (available from your App Store if you don't already have it) to accomplish this.
Once in the My Account App, navigate to the Internet section, tap on your Gateway and then choose "Troubleshoot" to get started.
Once the Gateway is back online, go to the Home section of the app, tap on your Touchscreen and choose "Troubleshoot" and then "Restart Touchscreen."
Once the Touchscreen is back up, test things out while you are at home by setting up a rule for a Push Notification (such as sending a notification when a door is opened) and then triggering the rule to see if it's sent to your phone in real-time.
I hope this helps!
Hi WesternLLC, (ComcastBecker) shared some great tips here. Have you been able to get this problem taken care of with the steps provided?