I'm not there to watch you, but if you're having a slow dip AND drive, then leg strength might be something to work on as well.
There are certain factors to keep in mind (back and stomach tight/locked down, short yet controlled dip, explosive drive and change of direction, aiming the bar towards the back of your neck), but if you feel you're slow, your squatting will help, in addition to maybe some jerk dip and drives with some heavier weights, jumping back squats, and heavy 1/4 squats.
The addition of those movements is getting into different philosophies and approaches (purists vs. others that prefer strengthening/auxiliary movements, Bulgarian vs. Russian/Chinese). In addition, you may end up loading yourself with way too much work and not allow yourself to recover properly. If you're on the 8-week general cycle because you're new to the sport and its movements, I wouldn't worry about altering your program; keep the course and see how things turn out after the eight weeks, then make adjustments off of that.
Hope that helps,
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.