It won't even trigger it, as Yubel can only summon ultimate nightmare if she's destroyed by card effect. So yea, tributing her with this effect won't cause her to summon it
OCG's ruling with Share the Pain vs Evilswarm Coppelia, ruled that Coppelia's effect (which is a "leave the field" effect like Terror Incarnate) does not activate.
So if they programmed it correctly, Share the Pain shouldn't trigger Terror Incarnate's effect.
Coppelia needs to be sent to the Graveyard by an opponent's card. It's not being sent to the Graveyard by Share the Pain. It's being sent by a game mechanic, similar to how a card like Rivalry of Warlords works.
Terror Incarnate isn't as picky about how it leaves the field. As long as it doesn't miss its timing (and doesn't get banished face-down/returned to the Deck), it'll trigger.
Ya boi Zorc
