Speed of progress depends on your dedication to your training and recovery, as well as your body’s ability to adapt to certain exercises. Could be anywhere from a couple of weeks to a number of months. Increasing your reps alone, especially from such low numbers, is an indicator of strength gains. I’d say 20 pull ups is more in line with about 10 pistols per leg. Explosiveness will come with strength, but you can train more specifically for it with plyometric exercises.