There are different parts to your question.
settng a delay
Smart home monitor, which is the “solution” in the official smart things mobile app, does not have a time delay to give you time to disarm. I’m not sure why. They may add it in the future.
There is a very popular community created smartapp, smart alarm, which does have the delay feature. So it’s definitely possible to have a delay with custom code, or by using smart alarm.
having two tones
As far as I know, the Aeotec siren cannot change sounds on the fly. Only as part of a full configuration. ( I don’t know if the doorbell is any different.)
You could definitely do it with two different devices. One that went off initially, and then one that went off after the delay using one of the delay methods in the section above.
So, I think you can do it in SmartThings, but it’s not as simple as just a built in setting on one of the alerts in the smart home monitor. It would take some custom work and it would probably take two devices unless there’s a particular siren that can change sounds on the fly.