check if the "rollout" trigger is configured on parent page and the cq:LiveSyncConfig node exist on child with appropriate configs?
In addition to that, validate that relevant Action Configs in /system/console/configMgr -- CQ MSM Content Update Action, Copy Action, Delete Action and CQ MSM Page Move Action, etc. have the appropriate configurations to allow your use case.
P.S. you may refer to we-retail implementation for a working example