The extra lessons after normal school time did come into the category of child minding, I agree. The rich parents preferred that the kids stayed in school and were willing to pay extra. All the hard work was done in the real school hours and the overtime was just an opportunity to socialise. Although it was originally intended as a baby sitting service, it proved to be really helpful in building teacher/ student relations. The kids would play football, swim or play that Thai game with a ball made of cane, and the teachers just supervised, joined in or sat about chatting.
It was all very pleasant and everybody, parents, teachers and kids, were all happy with the arrangement.