"Deidara does ignite from passive not mystery" yes, but right answer is still Deidara. It might be just a error in question.

There is a bug indeed, Deidara does extra damage to ignited enemies with a Prompt Mystery. It's a bad wording from the test
http://prntscr.com/dnfj2j

edit: dont know why but this forum always gives me troubles posting pics in the responses so here is the link
http://prntscr.com/dnfj2j This post was last edited by Glyrin at 2016-12-24 15:03 This post was last edited by Glyrin at 2016-12-24 15:03

I agree that it's a bit confusing, but as stated before the correct answer is Deidara.

It's mostly due to the fact that activating a prompt mystery, forces the character to activate any passive inducing effect.
An example would be Sailor Sakura, she has two debuff removes as a passive, before her mystery she removes a layer and the second one before her standard.

Deidara induces Ignite before his mystery.

Hope that helps.