At least for the ground beef taco seasoning, the meat is supposed to be fully (or at least mostly) cooked before adding the seasoning. You brown it first, drain off excess fat, then add the seasoning with water, and let it simmer for like 5 minutes or something. Since most ground beef has excess fat, you wouldn't want to drain off the spices when you drain the fat. The flavor packet + water ends up turning into a sort of sauce that flavors the meat.
Given that, I don't know that it matters whether your chicken is raw or cooked when you add the flavoring. Adding it to raw chicken is probably fewer steps, and works fine because chicken doesn't usually have a bunch of excess fat that needs to be drained. But since even cooking raw chicken in the spices isn't going to flavor anything but the outside of the chicken, adding the flavor packet to cooked chicken with a little liquid will turn it into a sort of sauce and probably accomplish more or less the same thing. However you cook your chicken, though, you probably want the pieces to be relatively small (since only the outside of them is going to get the benefit of the seasoning).
I also personally prefer shredded chicken over cubed when I need to have it in small pieces. It provides a maximum of surface area (so the meat gets very well-flavored by sauce) and it's often easier to eat thank even small chunks of chicken. If you cook the chicken and shred it while it's still hot, you can do it pretty easily with two forks (you just run them in opposing directions until all the meat is shredded). I've done it with bone-in and bone-out chicken, although it's easier with bone-out (for obvious reasons). It doesn't work very well on chicken that's cold, but you can refrigerate the shredded chicken for use later if you've made your chicken in advance.