I use a PAYG SIM, though not this particular dialler.
Most diallers allow a "status" SMS to be sent to it, which then triggers a response SMS back. The SMS dialler would only cost for the message it sends out, not the one it received to trigger it.
The status SMS can just respond with something simple, stating whether the alarm is currently on or not (depends on the dialler).
Sending one of those status SMS once a month or so is usually enough to keep the PAYG SIM active.
As mentioned already, it's best to have a PAYG SIM that can be registered and managed online, so that you can keep an eye on the balance and top up.
Why PAYG over pay monthly?
Once a dialler is set up correctly, there shouldn't be an expectation for it to make calls/send out lots of SMS on a regular basis (if it was, you might have other problems with false alarms being triggered etc).
Having a mobile contract for something used so infrequently would be a waste. As long as you make sure to keep the PAYG SIM active it can last a long time.
Example, lets say a PAYG SIM charges 10p/SMS, and you load it with £10
Even if you sent one status SMS a month, that £10 topup will last you for 100 months (over 8 years)
even at £5/month, a contract for the same period of 100 months would cost £500!