Anticipating the trigger happens because you are thinking about the trigger, rather than focusing on a mantra or pulling. If I'm pulling, and saying my mantra, but in another part of my mind I'm thinking, "this is hard to do, and I wish the trigger would happen, and it should be about ready to happen now", that defeats the purpose of saying the mantra and focusing on pulling. The purpose of saying the mantra and focusing on pulling is to take your attention away from the trigger, so that when it happens, it is a surprise.
Now you ask, how can I be surprised 1,000 times in a row, when the clicker (or whatever) happens at the same place every time I shoot? How could I NOT begin to anticipate it after a while? The answer is, you can't anticipate it if you're not thinking about it. The purpose of the mantra and focusing on pulling is to give your mind something else to do so you're not anticipating the trigger. Sometimes when Joel asks people what they were thinking about during the shot sequence, it's very difficult to respond, because it doesn't seem like they were thinking about anything; at least, that's the way it was for me. Sometimes, thoughts like, "this is getting hard to hold together and the clicker should be about ready to click," don't seem like thoughts at all, they just seem like an awareness of reality, so they're hard to recall. But those are the thoughts you want to get rid of. The first step in getting rid of them is to realize that they ARE thoughts and should be under your control, and not just a part of the environment around you. If you have those thoughts, it means that you need to focus more on whatever method you are using to avoid them, or if the method is ineffective, try a different one.
One thing that was effective for me was to accept that in each and every shot I make, there will come a point when it becomes difficult to hold the shot together. Before, I had a kind of dread of reaching that point, which made me want to rush to get the shot over with when I felt that point approaching. Which is kind of dumb, in a way. Why even do archery if you want to rush to get it over with? So I convinced myself to simply anticipate the tension as a normal part of the shot rather than dread it, and let myself experience it rather than avoid it. Just a subtle shift in point of view, but it has helped.