Once I've taken the unique Vigilante Talent to get a Ninja Trick, I can THEN take the Extra Ninja Trick feat to get more, correct?
no, your vigilante talent is that ninja trick, you don't have ninja tricks.
More specifically, although the teisatsu gains a access to a ninja trick by spending a vigilante talent, he does not have the "Ninja Tricks" class feature that is a prerequisite for the feat you want to pick up. Instead he has the Teisatsu Talents class feature that he has used to select a Shadow Trick.
A GM may house rule it to allow you to take extra ninja talents if you ask nicely (its not totally unreasonable).
Okay, so this is one of those looks like a duck, smells like a duck, but it's a subspecies of Swan. Sadness. Thank you guys.