And that Pavlovian response is to the very project's name. I'm no expert, but if it were me, I might have chosen a different fake location than the very project's name.
You're arguing from retrospect there. Remember, nobody in the show had any idea that "Tahiti" was the name of the project until they actually stumbled upon the sign saying T.A.H.I.T.I. -- well after
they'd learned of Coulson's resurrection and the project's existence. So the name Tahiti was never, at any point, a clue to the existence of the project; rather, all the other clues led them to the project that, as a final punch in the gut, turned out to be named T.A.H.I.T.I.
After all, there is
a real Tahiti which is famous as a paradisical vacation destination, so that in itself serves as a perfect red herring. The name would naturally lead people away from
the project rather than toward it. The clue was never the name -- the clue was how Coulson reacted to hearing the name. And if the conditioning had been more subtle and his reactions more natural, nobody would've suspected a thing.
...but I think a super-secret project with a triggered response to the project's name as a side-effect is a major problem.
Which is exactly my point: It was
a major flaw in the programming, one that tipped Coulson off that something was wrong and led him to seek the truth. People make mistakes. As the saying goes, never attribute to malice that which can be adequately explained by incompetence. Particularly where the exposure of secrets is concerned. The bigger a secret is, the harder it is to keep, simply because it is the truth and will always be the truth no matter how hard people try to hide it. So if people fail to keep a secret, that absolutely does not
prove that they wanted it to be discovered. Most of the time, it proves that no coverup is ever perfect.
Again: This is the first time the resurrection process actually worked. It makes perfect sense that there would be uncorrected bugs in the process. Therefore it makes no sense to assume that any flaw has to be there as a result of someone's deliberate design. The process isn't perfected enough to be that controllable.