They were driven by government policy, the policy was around changes in the schooling system + whatever changes were needed to encourage kids to go to school. The changes had NOTHING to do with “increase the returns to schooling” as Pritchett wrongly asserts.
Were these increases typically driven by public demand
This is really hard to tell. If there are no schools in walking distance of your village and hence no one goes to school does it mean there is no demand? If you live in an authoritarian country and know that the dictator will not build schools, and hence no one demands schooling. Is there no demand?
In the case of Kerala, Singapore local governments did all they could to encourage schooling. As a result enrollment increased. Does that mean there was an increase in public demand? (Edit: The governments of Kerala, Singapore also built the schooling system: building, teachers, books etc...)
Disentangling government action vs public demand is not so important. There are good practices from Singapore, Kerala etc… that can be learnt by governments the world over.