Somewhere in the FAQ they indicate that NIST and the US Navy sync their clocks every 10 minutes. I'd wager that is why they refresh the webpage at that same frequency.
I've repurposed a couple old iPhones and a 2nd Gen iPad as baby monitors using the aptly-named Baby Monitor app (no affiliation other than being a satisfied customer). One sits in the kid's room as the mic/camera and the others serve as the speakers/display. The app is fantastic as it works on essentially any version of iOS and any iOS device. The iPad chokes on any website and barely runs anything else, but works perfectly with the Baby Monitor app.
I wish more apps like this worked on older versions of iOS or Android. No need to hack around with some alternative OS (not that there's anything wrong with that) - it's usable by any non-techie with some old iOS devices.