I'm the author of the service.
This is a fundamental limitation of the network as opposed to a shortcoming of the service. When you submit a transaction, it is up to the miners as to whether it gets included in the next block. There are lots of factors that go into this decision, and in normal situations, transactions are going to get included in a block very quickly.
If you accept the assumption that there are enough people executing calls (in exchange for $$) and that the network is not so flooded with transactions that miners are having to exclude them due to volume, then the likelihood that your function won't be called drops near zero.
If the network is congested with too many transactions, then it doesn't matter if the call was triggered by the alarm service or somewhere else, it will still have to compete to be included in a block just like any other transaction.
Now if you want to talk about selective censorship of function calls, then that is an interesting attack vector that I'd love to chat about.