Rules that pin/promote items created via the Magento Admin Page and managed via the extension are not pushed/forwarded to the replicas, by default. You can customise this setting here.
Query Rules that can be set up on the Faceting section of the InstaSearch Results Page configuration settings on the Magento Admin are pushed/forwarded to the replicas, by default. You can customise this setting here.
Rules that are manually created in the Algolia Dashboard will follow the "Forward to replicas" setting on the rule.
As per our documentation here, every time a new replica is created it will inherit all data and settings of the primary replica, including all of the rules. In this case you will have to manually delete any unwanted rules from your new replica indices. Those rules will not reappear after a reindex (unless it is a facet Query Rule).