Hi, there is no hard and fast rule on when is the right time. Both my LOs have been sleeping on babysafe pillow since young and now they are toddlers and chose to sleep on the adult pillows.
The idea of a pillow is to elevate their head so there will be better blood circulation at night.
Having said that, I do have friends' children who have not slept in pillow at all and they are in their teens and doing well too. So ultimately, it is a choice.