when I make some radical setting like detune or a fast response, there is no difference
Just to make sure it's working, maybe you should try something even more radical. At the top center of the Pitch Correction window, there are two menus, Root and Scale. By default, they are set to 'none' and 'chromatic.' Click on 'chromatic.' Scroll all the way down and select the last item, 'single.' Root will now say 'C.' While playback is cycling, experiment with different settings for Root. Still hear no difference?
Also, make sure to do what CCT said and set Response to 0.00ms.
Also, look at the meter at the bottom center of the window. It's called "Correction Amount." See anything moving there?
the notes are lighting up
That means the plugin is not bypassed.
By the way, are you sure you're listening to the right thing? If the track hosting the plugin is muted, the plugin will still light up, and you could be hearing the dry material if a copy of it happens to be playing back from another track entirely.
You should carefully identify which track is hosting the plugin, and make sure to solo only that track. Option-click on the solo button for that track.
Also, is an aux hosting the plugin? Are you sure you are hearing all wet signal and no dry signal?
If you're having a hard time making sense of these questions, then it might help to post a screenshot of your mixer. If you need help understanding how to do that, just ask.