This is what happens when I work too many long hours in a row and I don't write
down well thought out responses. First of all I have no business trying to
explain technical things over the internet because it is usually an exercise in
futility. What it requires is dojo time with your teacher.

I want to take back what I said earlier. Or at least modify it somewhat. Both
ways are correct. It's just a matter what you are doing in your head. Are you
doing it as 2 distinct movements or 1? I was taught to do it as 1. Otsuka
Sensei did it as one. So does most of his senior students. These kata takes
time to learn and maintain. That's why people who know what they are doing
sometimes end up doing things slightly different at different times. Let me
attempt to deconstruct that kette junzuki plus gyakuzuki bit. (I can hear
Gordon in my ear chastising me ..lol) If you focus on the gyakuzuki then you
miss why the gyakuzuki doesn't work. If the technique before is not set up
correctly then the next one won't be as effective. The key to the gyakuzuki is
how you do the kette junzuki. I am making tons of assumption here once again
but you need to drive the junzuki with the knee of the leg you just kicked with.
You kick, retract sharply, then you must drive the same knee forward to move the
whole body forward so the punch has your entire body behind it. When the front
foot plants as a result of the knee driving the body the punch is done. ( Of
course if you land too long then you can't cut your hip because your hip will be
too open.) If you do not drive with your body then your punch is limp and
meaningless so the gyakuzuki follow is also dead. And after you stick that
punch you have to know how to relax it immediately because the retraction
(hikite) drives the gyakuzuki. If tension remains in the junzuki punch then the
gyakuzuki comes out stiff and slow and therefore weak. And of course unless you
know how to cut your hip the gyakuzuki still won't work as effectively. No knee
thrust(body drive) from the kette junzuki then no good gyakuzuki.

This is one techique done in 3 movements. 1)Kette 2)junzuki 3)gyakuzuki. It is
not 2 movements. At least that is the idea that was driven into my head for
years. So someone is going to ask how one would explain the 3rd and 4th
movement of Chinto where there is a distinct shift of the feet when you go from
naname heikodachi to tate seishan. I don't know.......But I think I can do it
right...mileage may vary depending on the day of the week.

If you are still reading this then you are a major karate nerd...

This stuff can't be worked out over the internet. It can only be worked out in
your dojo with your teacher. So why do I bother? Must be my medication.