yep you have to warm up before making an all out effort, that's a given
I'd also heard that fellas who did do AJ's full body wo 3 times a week made ggains on the legs but not elsewhere so much because they always did do legs first so after that effort their energy/power was shot and they couldn't put the necessary effort into upper body work after that
A fellow who worked at Nautilus by the name of Joe Mullen had a very logical approach to alleviate this inherent problem with Jones' HIT (a problem I experienced myself). Simply put, you evaluated each full body workout grading each exercise that you did. Whichever exercise you did worst at, you trained first the next workout, with the best exercise from the previous workout being performed last. My brother (who competed at NPC Nationals a number of times) commented to me that my training made me bigger, but that I was too balanced, nothing had a "wow" factor. FYI, I was always natural, so I used to retort that maybe there was a key difference between my training and his (one he would never acknowledge).
Mullen recommended using compound movements almost exclusively, and to really only focus on single joint rotary movements if one were glaringly weak in an area, or if one were getting ready for a contest. I can tell you that his method produced very good results for me when I was working crazy hours (70+ week) and was only training Monday and Friday of one week, then Wed. of the following week.
Another way around the problem many faced with Jones' training recommendation that I have used personally is to train the smaller bodyparts first as a warm up to the bigger compound movements. I would start some of these workouts with movements such as 4-way neck, bicep curls (which never seem to get adequately directly worked in a true Nautilus program as they are only done towards the end of a workout) tricep, calves.