This situation happened in one of Andrea Mengucci's recent videos.
Mengucci had Omniscience and Dress Down in play. He then decided to cast Emrakul, the Aeons Torn in case opponent made him shuffle his hand into his deck, but was surprised when Emrakul triggered and he got an extra turn.
Why did Emrakul trigger? With Dress Down in play, it ought to have no abilities, including the cast trigger. Relevant text of cards:
Creatures lose all abilities.
When you cast this spell, take an extra turn after this one.