Controlling these alerts is not a feature that you will find in any 3rd party SMS apps.
With almost all carriers/devices, Amber Alerts, and the like, are not normally SMS messages. They are simply delivered through your stock messaging app or at the system level. They just do it this way, because your stock SMS app is the usual connection between your carrier and their network.
If they are being received to Pulse SMS, then they would be coming in as an SMS, from a phone number. If they are coming through Pulse SMS, the alert wouldn't give you the blaring alert sound that most people think of for these alerts. Pulse SMS would give you a normal Pulse SMS notification, since it just knows you received a new message. If they are within Pulse SMS, you could blocklist the sender to turn them off, just like any other conversation/number, to prevent the messages from reaching you.
If you wanted to turn them on, you would need to do so through other means (system level settings, the stock app that came with your phone, or whatever other means you have used in the past).
