That video is SOOOO miss leading.
Because what is going on really is the guy is playing a very
slow tune. He only SAYS the word as he plays the note. Nobody performing has the piano player hitting the note they are singing, except at church. In church the organ player drowns out the choir generally anyway.
What the heck are you going to do for a fast tune to stay in tune?
The part of your question of just hearing the BACKUP harmony without your voice, forget that idea with the VH2 on Yamaha keyboards, it will always sound like a ROBOT with breakups in it to boot.
You have to sing in key with the VH2 and that ability just takes practice.
Maybe a newer Harmonizer the pros use can help you out, I don't know. But I was watching the Rose Bowl Parade on New Year Day and the opening act was a singer named, Chaka Khan. The first part of her song, the Vocal Correction wasn't ON and it was a total JOKE. My wife even commented. "who told her she could sing."
When the KTLA tv showed the replay of the parade, guess what? They CUT OUT that first part of her singing so badly.
Just pointing out there is equipment that can assist you, I just don't know what it is or how much it will set you back.
Regards
Drake