It is technically possible for composting to take place in the solids container (you have all the ingredients required – carbon, nitrogen, water and air), but most users won’t have the contents sitting in the solids container for a long enough period of time.
For most people, you would use the toilet until it is full, at which point some of the contents will have started breaking down, but a lot will still be ‘fresh’. This will need composting away from the toilet for an absolute minimum of six months, ideally twelve months.