If PagerDuty goes "ding" at 3am, it's probably best to take a look.
If Slack goes "ding" at 3am, maybe you forgot to turn off notifications or something, but by no means do you need to even read the notification.
When they were the person on-call, or only when they actually responded to an outage? Unless outages are really that infrequent, it pays to set clear boundaries on when and who is supposed to be available for an outage, and the cost of a dedicated solution like Pagerduty (or Grafana OnCall) is negligible.
I imagine it’s possible but that seems like a terrible idea. Making the compensation for being on-call obvious seems better for everyone involved. At least the one who might have to get up on Christmas know exactly what they are getting out of it and that no one is taking advantage of them in the rotation.
It really depends on the scale of the business. In some large ones, there is always a person working to handle “must be fixed now” problems. If you are off shift, then it is the person on shift’s task.
In smaller operations with 24 hour operation, and infrequent “must be fixed now” problems, there will be workers whose job includes being on call. Sometimes the on call duty rotates, sometimes it does not.
So if you are from a land of large companies, it may seem insane for your employer to ask something of you outside your shift. Likewise, when you are a little guy scrambling to grow, getting out of bed once in a while and handling a problem to preserve that growth is your best option.
In the situation in this post, I would hope that the critical “get up and fix this” messages come through a different system, or have a way to cut through a “do not disturb” so the employees can mute the mundane messages.
It sounds like you are in the first group. My company didn’t staff 24 hours, but used to pay people extra when they were the “get up and handle this” person. The size of the pay, and the frequency of the events was tuned so there was always a willing pool of people queueing to be the pager carrier.