I wouldn't say kids that start intense sports tend to be short. I've been playing since I was 3, more intensly since about 7 or 8, and I'm 6'3''. You do have to be careful of the weight room at an early age. Lifting heavy weights when your body hasn't has a chance to develop can stunt your growth, but playing tennis seriously definitely will not.
Atatu, I would start your son now if he is interested. Make sure the pro keeps in competitive and FUN!! No matter how good he gets, it has to be fun between ages 7-13, otherwise there is a big chance of burning out. Hopefully it will be fun the whole time, of course. But after 12, if the kids are very keen to get better and make something of it, the hard core training can start.