From my experience, as soon as you take the step that results in the drum's appearance to the right of the school, the task is complete. You can beat the drum at any time and all the children gather (although those coming from the inland side of the island sometimes have a hard time getting around the building).

I experimented with the drum a bit to see if it has any effect on the extent of skills that the nursing babies have once their mothers drop them (as in, the more times you summon the children to school, the more skilled the babies are when they become independent), but there seems to be no effect. I'm trying to figure out why some children are more highly skilled at 2 than others. Perhaps it has to do with how skilled their parents are?