There’s a chance you might not notice it for sure, though most can tell immediately when they get put in front of a standard 60hz display. It might be worth a look at the UFO test for both your eyes and monitor. It should be very noticeable if your eyes are doing the tricking, or the monitor isn’t performing correctly on that site. If you have a newer phone that has a 90hz+ display, you can also use that as a sanity check.
I haven’t heard of that site before and their writing seems… odd. Theres still a couple things that it could be, though they get more funky. It could be that FRC is enabled on the monitor, which on some caused issues with high refresh rate, or adaptive sync (gsync/freesync). It could also (still, if you’re unlucky) be the cable, or port on your GPU, or the GPU itself if it doesn’t support Display Stream Compression if it’s too old. There’s also a chance that the GPU straight up can’t do 4k while your settings are set to 120hz, or vice versa, or even more fun, it might claim to be doing one of those, while doing neither (or just one, but saying it is doing both/neither). Monitor issues are the worst lol.
Anyways, sorry if I couldn’t help. I’m certain there’s a pretty good chance it is not your eyes, but between Windows… being as it is, and monitors being notoriously annoying to diagnose, it’s not a fun one to track down.