What happens when I summon "Gameciel the Sea Turtle Kaiju" to my opponent's field by tributing their "Prank-Kids Battle Butler"?
As far as I'm aware, there's no specific ruling issued for this sort of interaction yet, but to the best of my knowledge I would say:

No, the effect of Battle Butler will not activate.

So, there's a little bit of a distinction we have to make here to understand why this one works the way it does. It's a bit nuanced.

Gameciel is not sending Battle Butler to the GY in this scenario. The player who summons Gameciel is tributing it as part of a summoning procedure.

This is in important distinction; Gameciel itself is not tributing the card; you, the player are tributing it. Semantically, it's the same reason why the monsters used for a Tribute Summon, or tributed to summon something like Raviel, Lord of Phantasms are not considered to be sent to the GY by the monster they were tributed to summon.