One point I think I wasn’t clear on: the notification I asked about was received while browsing from my computer. I don’t visit the site using my phone, which is why I was puzzled and asked about it.
The Tapatalk notification triggers on Chrome regardless of the device, so it will trigger on a PC.
I don’t remember it triggering on Firefox. I don’t think it does but not 100 percent certain on that. I know it triggers on Opera, Blackberry (anyone still use those?), iPhones and iPads. Maybe Kindle, not sure.