Does my Supernote and Mac have to be on the same Wi-Fi for notes?

Yes, for anything that reads the device live — first-time opening a note, and pulling a newer version. The app finds your Supernote by looking for it on your local network, so both devices must be on the same Wi-Fi (and Browse & Access on). Once a note has been saved, viewing that saved copy works with no Wi-Fi and no device at all.