The central idea of explosive training is that is utilizes the anaerobic alactic energy system. This energy system has enough ATP for about 7s of sustained high intensity exercise. This is the system that the fast-twitch muscle fibers use. After 7s, there is not enough ATP for sustaining contraction and the muscle switches to the anaerobic glycolytic (less capable of generating force, and produces lactic acid which inhibits contraction).
To answer your question there are three aspects that have to be taken into consideration
1) Duration of contraction
- The contraction should not last longer than 7-10s. That means that you would do about 9-10 jump squats in a set, about 7-8 chin ups etc.; you are constrained by a time limit, not a number of reps.
2) Force of contraction
- The force of the contraction has to be as high as possible. The best way to achieve this is to increase the weight which you exercise with. However, since you are doing bodyweight exercises only, the execution is crucial for adaptation to occur, since after a couple of weeks your muscles will get used to the training stimulus and no further increase in strength, hypertrophy or explosiveness will occus. To activate as many motor units as possible (=a greater part of the muscle) you have to perform the exercise as quickly as possible. I.e. try to do as many reps as possible within those 7-10s. Just make sure you use the proper form; don't cheat your way to a higher rep count.
3) Number of sets
- When training the anaerobic alactic system you do not have the same adaptation mechanisms as during hypertrophy training. When aiming for bulk, you do 3 sets of 8-12 reps at 4 seconds per rep, totalling a set time of about 40s. However, when training for explosiveness, you do not produce lactic acid, and the muscle does not fatigue as easily, so you have to perform more sets than for hypertrophy.
- Firstly because of the lower volume of training; the total number of reps per training is much lower when doing explosive training than for hypertrophy.
- Secondly, the muscle hardly fatigues, so theoretically you could perform as many sets as 15-20 or more. In my training (I am a professional sprinter), I usually keep doing sets until my form deteriorates, which usually occurs somewhere around the 7th-9th set depending on the muscle.
So to answer your second question directly, you do not cross over to endurance training by increasing set number, because you actually rest between the sets. You increase the endurance aspect of training by increasing the number of reps within each set. Just make sure you have about 5min of rest between sets so that your ATP has time to replenish.