Forum:Zombie World, Soul-Absorbing Bone Tower, and Substitoad

On the Frogs page, there is a OTK idea that has Zombie World and Soul-Absorbing Bone Tower on the field while Substitoad switches out another monster to mill the opponent's deck till game. Specifically, Substitoad pulls a frog monster. An example is below:

Zombie World is active. Soul-Absorbing Bone Tower, Substitoad, and any other monster is on the player's field. Using Substitoad's effect, the player tributes the "other monster" and pulls out a frog. Soul-Absorbing Bone Tower's effect activates because a Zombie-type monster was Special Summoned. By tributing the frog monster, and pulling out another, the player can continue this until there are no cards in the opponent's deck.

My friend says that this idea will not work because while Zombie World turns monsters on the field and in the graveyard into Zombies, as well as DNA Surgery turns monsters to a given type while on the field, During their Special Summoning, they are the origional type.

Cards that this could affect include Gladiator Beasts, Monster searchers such as Masked Dragon, and Substitoad. I cannot find a ruling stating specifically when a monster Special Summoned from the deck has its type changed, during the Special Summon or immediately after.

Can anyone find a ruling that states when a monster would have its type changed, or if Soul-Absorbing Bone Tower would activate its effect for a frog being Special Summoned?

I would like a specific ruling for this, if possible.