Titania attacked him at the beginning of Small Favor before Mab even shows up. He's not her Emissary at that point. He has to take the job. He has no standing in Winter at that time. Titania may simply want him dead for Aurora. Those guys also chased various Carpenters... they are not emissaries.
The tense of the phrase when Mab talks to Harry in the snow storm is past tense.
“I have chosen you to be my Emissary,” Mab said to me. “You will repay me a favor owed. You will find the Baron.
Not I will choose, but I have chosen. Which is why the Gruff's attacked at Michael's.
Butcher sets this up in Summer Knight by establishing that the Queens can't just attack any mortal they choose. Which is why the chlorofiend can't hurt Murphy in Summer Knight. He goes to a lot of trouble to establish this. For Titania to attack Harry he has to be connected to Summer in some fashion. That connection doesn't exist until Harry is named Emissary. It's explains the doughnut. When Harry gets back to Chicago the Emissary's work is finished and Harry is again safe.
This is actually her second run at Harry. She uses her position as a Fate to choose for Harry to die in the alley behind Bock's Books in Dead Beat. When Marcone interferes Titania uses this fact to attack him in Small Favor.
“This is another point of contention between you and Titania.”
“When one Court moves, the other perforce moves with it,” Mab said.
I croaked, “Titania wants Marcone dead?”
“Put simply,” she replied. “And her Emissary will continue to seek your death. Only by finding and saving the Baron’s life will you preserve your own.”
This arc effectively ends when Titania gives up her quest for vengeance in Cold Days. It also has ramifications for Proven Guilty and helps explain why Mab is defending her borders.